Proportion / Ratio / Rate - SAT Math
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A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
After watching 12 minutes of the show 18 remain. 18 is 60% of the total 30 minutes. As a fraction it can be expressed as 3/5.
After watching 12 minutes of the show 18 remain. 18 is 60% of the total 30 minutes. As a fraction it can be expressed as 3/5.
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A bag contains red, orange, and yellow marbles only. The marbles occur in a ratio of 5 red marbles: 4 orange marbles: 1 yellow marble. If one-third of the red marbles, one-half of the orange marbles, and one-fourth of the yellow marbles are removed, then what fraction of the remaining marbles in the bag is red?
A bag contains red, orange, and yellow marbles only. The marbles occur in a ratio of 5 red marbles: 4 orange marbles: 1 yellow marble. If one-third of the red marbles, one-half of the orange marbles, and one-fourth of the yellow marbles are removed, then what fraction of the remaining marbles in the bag is red?
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Marty drove 40 mi/hr for 3 hours, then 60 mi/hr for 1 hour, and finally 70 mi/hr for the last 2 hours. What was Marty's average speed?
Marty drove 40 mi/hr for 3 hours, then 60 mi/hr for 1 hour, and finally 70 mi/hr for the last 2 hours. What was Marty's average speed?
Marty's total driving time was 3 + 1 + 2 = 6 hours. He drove 40 mi/hr for 3 hours, or 3/6 = 1/2 of the time. He drove 60 mi/hr for 1 hour, or 1/6 of the drive. Lastly, he drove 70 mi/hr for 2 hours, or 2/6 = 1/3 of the drive.
To find the average speed, we need to multiply the speeds with their corresponding weights and add them up.
Average = 1/2 * 40 + 1/6 * 60 + 1/3 * 70 = 53.33... ≈ 53 mi/hr
Marty's total driving time was 3 + 1 + 2 = 6 hours. He drove 40 mi/hr for 3 hours, or 3/6 = 1/2 of the time. He drove 60 mi/hr for 1 hour, or 1/6 of the drive. Lastly, he drove 70 mi/hr for 2 hours, or 2/6 = 1/3 of the drive.
To find the average speed, we need to multiply the speeds with their corresponding weights and add them up.
Average = 1/2 * 40 + 1/6 * 60 + 1/3 * 70 = 53.33... ≈ 53 mi/hr
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A pie is made up of 
crust, 
apples, and 
sugar, and the rest is jelly. What is the ratio of crust to jelly?
A pie is made up of
A pie is made up of 
crust, 
apples, 
sugar, and the rest is jelly. What is the ratio of crust to jelly?
To compute this ratio, you must first ascertain how much of the pie is jelly. This is:
Begin by using the common denominator 
:
So, the ratio of crust to jelly is:
This can be written as the fraction:
, or 
A pie is made up of
To compute this ratio, you must first ascertain how much of the pie is jelly. This is:
Begin by using the common denominator
So, the ratio of crust to jelly is:
This can be written as the fraction:
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In a solution, 
of the fluid is water, 
is wine, and 
is lemon juice. What is the ratio of lemon juice to water?
In a solution,
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
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If 
and 
, what is the ratio of 
to 
?
If
To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:
Recall that division of fractions requires you to multiply by the reciprocal:
,
which is the same as:
This is the same as the ratio:
To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:
Recall that division of fractions requires you to multiply by the reciprocal:
which is the same as:
This is the same as the ratio:
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A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
A TV show lasts 30 minutes, what fraction of the show is left after 12 minutes have passed?
After watching 12 minutes of the show 18 remain. 18 is 60% of the total 30 minutes. As a fraction it can be expressed as 3/5.
After watching 12 minutes of the show 18 remain. 18 is 60% of the total 30 minutes. As a fraction it can be expressed as 3/5.
Compare your answer with the correct one above
A bag contains red, orange, and yellow marbles only. The marbles occur in a ratio of 5 red marbles: 4 orange marbles: 1 yellow marble. If one-third of the red marbles, one-half of the orange marbles, and one-fourth of the yellow marbles are removed, then what fraction of the remaining marbles in the bag is red?
A bag contains red, orange, and yellow marbles only. The marbles occur in a ratio of 5 red marbles: 4 orange marbles: 1 yellow marble. If one-third of the red marbles, one-half of the orange marbles, and one-fourth of the yellow marbles are removed, then what fraction of the remaining marbles in the bag is red?
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Marty drove 40 mi/hr for 3 hours, then 60 mi/hr for 1 hour, and finally 70 mi/hr for the last 2 hours. What was Marty's average speed?
Marty drove 40 mi/hr for 3 hours, then 60 mi/hr for 1 hour, and finally 70 mi/hr for the last 2 hours. What was Marty's average speed?
Marty's total driving time was 3 + 1 + 2 = 6 hours. He drove 40 mi/hr for 3 hours, or 3/6 = 1/2 of the time. He drove 60 mi/hr for 1 hour, or 1/6 of the drive. Lastly, he drove 70 mi/hr for 2 hours, or 2/6 = 1/3 of the drive.
To find the average speed, we need to multiply the speeds with their corresponding weights and add them up.
Average = 1/2 * 40 + 1/6 * 60 + 1/3 * 70 = 53.33... ≈ 53 mi/hr
Marty's total driving time was 3 + 1 + 2 = 6 hours. He drove 40 mi/hr for 3 hours, or 3/6 = 1/2 of the time. He drove 60 mi/hr for 1 hour, or 1/6 of the drive. Lastly, he drove 70 mi/hr for 2 hours, or 2/6 = 1/3 of the drive.
To find the average speed, we need to multiply the speeds with their corresponding weights and add them up.
Average = 1/2 * 40 + 1/6 * 60 + 1/3 * 70 = 53.33... ≈ 53 mi/hr
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A pie is made up of crust, apples, and sugar, and the rest is jelly. What is the ratio of crust to jelly?
A pie is made up of
A pie is made up of crust, apples, sugar, and the rest is jelly. What is the ratio of crust to jelly?
To compute this ratio, you must first ascertain how much of the pie is jelly. This is:
Begin by using the common denominator :
So, the ratio of crust to jelly is:
This can be written as the fraction:
, or
A pie is made up of
To compute this ratio, you must first ascertain how much of the pie is jelly. This is:
Begin by using the common denominator
So, the ratio of crust to jelly is:
This can be written as the fraction:
Compare your answer with the correct one above
In a solution, of the fluid is water, is wine, and is lemon juice. What is the ratio of lemon juice to water?
In a solution,
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:
Remember, to divide fractions, you multiply by the reciprocal:
This is the same as saying:
Compare your answer with the correct one above
If and , what is the ratio of to ?
If
To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:
Recall that division of fractions requires you to multiply by the reciprocal:
,
which is the same as:
This is the same as the ratio:
To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:
Recall that division of fractions requires you to multiply by the reciprocal:
which is the same as:
This is the same as the ratio:
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Out of 85 students in a certain class, 42 own a laptop and 54 own an mp3 player. If 5 students don't own either, what fraction of the students own both a laptop and an mp3 player?
Out of 85 students in a certain class, 42 own a laptop and 54 own an mp3 player. If 5 students don't own either, what fraction of the students own both a laptop and an mp3 player?
Once you subtract the 5 students that don't own either, there are 80 students left.
There's 96 total students when you add the number that own an mp3 and the number that own a laptop, meaning 16 own both.
Recall that the fraction will be number of students who have both laptop and mp3 divided by the total students in the class.
Once you subtract the 5 students that don't own either, there are 80 students left.
There's 96 total students when you add the number that own an mp3 and the number that own a laptop, meaning 16 own both.
Recall that the fraction will be number of students who have both laptop and mp3 divided by the total students in the class.
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To ship a package, the postal service charges 
for the first 150 grams and 
for each additional 50 grams or part thereof. What is one possible weight in grams for a package that costs 
to ship?
To ship a package, the postal service charges
The weight will be 150 grams + (1.15 – 0.55)/0.05 * 50g.
You need to subtract first 150 grams cost from the total cost and divide by the price per unit to determine how many units. Next, multiply units by weight per unit and add to the original first 150 grams.
150 + 600 = 750 grams
This is the maximum weight that can be sent at that price; the minimum weight that could be charged this price would be 701 grams. Hence a package weighing 750 grams will be charged $1.15.
The weight will be 150 grams + (1.15 – 0.55)/0.05 * 50g.
You need to subtract first 150 grams cost from the total cost and divide by the price per unit to determine how many units. Next, multiply units by weight per unit and add to the original first 150 grams.
150 + 600 = 750 grams
This is the maximum weight that can be sent at that price; the minimum weight that could be charged this price would be 701 grams. Hence a package weighing 750 grams will be charged $1.15.
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The price of 10 yards of fabric is c cents, and each yard makes q quilts. In terms of _q_and c, what is the cost, in cents, of the fabric required to make 1 quilt?
The price of 10 yards of fabric is c cents, and each yard makes q quilts. In terms of _q_and c, what is the cost, in cents, of the fabric required to make 1 quilt?
We create a conversion ratio that causes yards to cancel out, leaving only cents in the numerator and quilts in the denominator. This ratio is ((c cent )/(10 yard))((1 yard)/(q quilt))=(c )/(10q ) cent⁄quilt . Since the ratio has cents in the numerator and quilts in the denominator, it represents the price in cents per quilt.
We create a conversion ratio that causes yards to cancel out, leaving only cents in the numerator and quilts in the denominator. This ratio is ((c cent )/(10 yard))((1 yard)/(q quilt))=(c )/(10q ) cent⁄quilt . Since the ratio has cents in the numerator and quilts in the denominator, it represents the price in cents per quilt.
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Susan is doing a bake sale for her sorority. One third of the money she made is from blueberry cupcakes, which cost 50 cents each. A quarter of her sales is from cinnamon cream pies, which cost $1 each. And the rest are from her chocolate brownies, which cost 25 cents each. She made a total of $60 at the end of her bake sale, how many brownies did she sell?
Susan is doing a bake sale for her sorority. One third of the money she made is from blueberry cupcakes, which cost 50 cents each. A quarter of her sales is from cinnamon cream pies, which cost $1 each. And the rest are from her chocolate brownies, which cost 25 cents each. She made a total of $60 at the end of her bake sale, how many brownies did she sell?
1/3 of sales from cupcakes = $20, ¼ of sales from cream pies = $15 and the rest are from brownies = $60-$20-$15 = $25. Since each brownie costs 25 cents, Susan will have sold 100 of them.
1/3 of sales from cupcakes = $20, ¼ of sales from cream pies = $15 and the rest are from brownies = $60-$20-$15 = $25. Since each brownie costs 25 cents, Susan will have sold 100 of them.
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In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly?
In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly?
Consider
(Bill + 7) = 2 x (Amy + 7)
(Amy – 2) = 1.5 x (Molly – 2)
Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.
Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1
Substitute this into the first equation:
(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12
Solve for Molly:
Bill + 7 – 12 = 3 x Molly
Molly = (Bill – 5) ¸ 3
Substitute Bill = 29
Molly = (Bill – 5) ¸ 3 = 8
Consider
(Bill + 7) = 2 x (Amy + 7)
(Amy – 2) = 1.5 x (Molly – 2)
Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.
Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1
Substitute this into the first equation:
(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12
Solve for Molly:
Bill + 7 – 12 = 3 x Molly
Molly = (Bill – 5) ¸ 3
Substitute Bill = 29
Molly = (Bill – 5) ¸ 3 = 8
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When Christina opens a bag of white and milk chocolate pieces, 20% of the chocolate pieces are white. After Christina eats 10 milk chocolate pieces, the ratio of brown chocolate to white chocolate is 2 to 3. How many pieces of chocolate are left in the bag?
When Christina opens a bag of white and milk chocolate pieces, 20% of the chocolate pieces are white. After Christina eats 10 milk chocolate pieces, the ratio of brown chocolate to white chocolate is 2 to 3. How many pieces of chocolate are left in the bag?
Let original white chocolate pieces = W and original milk chocolate pieces = M. So the total number of pieces in the original bag is M + W.
From the first sentence: (M + W) x 0.2 = W or
0.2 M = 0.8 W or \[M = 4W\]
Once Christina has eaten 10 milk chocolate pieces, there are W pieces of white chocolate, (M – 10) pieces of milk chocolate and (M + W – 10) pieces total. According to the second sentence:
W ¸ (M – 10) = 3 ¸ 2
Or 2W = 3M - 30
Insert the equation in brackets: 2W = 3\[4W\] + 30 = 12W – 30
10W = 30 or W = 3 and M = 12
We want “How many pieces of chocolate are left in the bag” or (M – W – 10).
So (M +W – 10) = 3 + 12 – 10 = 5
Let original white chocolate pieces = W and original milk chocolate pieces = M. So the total number of pieces in the original bag is M + W.
From the first sentence: (M + W) x 0.2 = W or
0.2 M = 0.8 W or \[M = 4W\]
Once Christina has eaten 10 milk chocolate pieces, there are W pieces of white chocolate, (M – 10) pieces of milk chocolate and (M + W – 10) pieces total. According to the second sentence:
W ¸ (M – 10) = 3 ¸ 2
Or 2W = 3M - 30
Insert the equation in brackets: 2W = 3\[4W\] + 30 = 12W – 30
10W = 30 or W = 3 and M = 12
We want “How many pieces of chocolate are left in the bag” or (M – W – 10).
So (M +W – 10) = 3 + 12 – 10 = 5
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You are buying a new car. The car gets 33 miles per gallon in the city and 39 miles per gallon on the highway. You plan on driving 30,000 miles over three years and 10,000 of that will be city driving. If gas costs $3.50 per gallon, how much will you pay in gas over the three year period (round to the nearest cent)?
You are buying a new car. The car gets 33 miles per gallon in the city and 39 miles per gallon on the highway. You plan on driving 30,000 miles over three years and 10,000 of that will be city driving. If gas costs $3.50 per gallon, how much will you pay in gas over the three year period (round to the nearest cent)?
Cost = ( Miles driven / Miles per gallon) * 3.50
Total Mileage = City Miles + Highway Miles
30,000 = 10,000 + Highway Miles
Highway Miles = 20,000
Cost City = ( 10,000 miles / 33 miles per gallon ) * 3.50
Cost City = 303.03 * $3.50 = $1060.60
Cost Highway = ( 20,000 miles / 39 miles per gallon ) * 3.50
Cost Highway = 512.82 * $3.50 = $1794.87
Total Cost = Cost City + Cost Highway = $1060.60 + $1794.87 = $2855.47
Cost = ( Miles driven / Miles per gallon) * 3.50
Total Mileage = City Miles + Highway Miles
30,000 = 10,000 + Highway Miles
Highway Miles = 20,000
Cost City = ( 10,000 miles / 33 miles per gallon ) * 3.50
Cost City = 303.03 * $3.50 = $1060.60
Cost Highway = ( 20,000 miles / 39 miles per gallon ) * 3.50
Cost Highway = 512.82 * $3.50 = $1794.87
Total Cost = Cost City + Cost Highway = $1060.60 + $1794.87 = $2855.47
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A class room of 8th graders is 1/3 boys. Of all the students 4/5 of them are aged 14 while the others are aged 13. If there are 20 girls in the class, approximately how many boys are age 13?
A class room of 8th graders is 1/3 boys. Of all the students 4/5 of them are aged 14 while the others are aged 13. If there are 20 girls in the class, approximately how many boys are age 13?
If 20 students are girls, this is 2/3 of the class, giving 30 students total with 10 of them being boys. 4/5 of the boys will be 14, leaving 1/5 of the boys age 13. 1/5 of 10 is 2.
If 20 students are girls, this is 2/3 of the class, giving 30 students total with 10 of them being boys. 4/5 of the boys will be 14, leaving 1/5 of the boys age 13. 1/5 of 10 is 2.
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