Fractions - PSAT Math
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A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
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The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
Alan is twice as old as Betty. He will be twice as old as Charlie in 10 years. If Charlie is 2 years old, how old is Betty?
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If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.
The ratio of 10 to 14 is closest to what value?
The ratio of 10 to 14 is closest to what value?
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Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
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?
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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
In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?
In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?
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The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.
To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.
The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.
To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
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1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
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15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
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Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
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1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
If you live 3 miles from your school. What average speed do you have to ride your bike get to your school from your house in 15 minutes?
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The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
The best way to find speed is to divide the distance by time. Since time is given in minutes we must convert minutes to hours so that our units match those in the answer choices. (3miles/15min)(60min/1hr)=12miles/hr; Remember when multipliying fractions to multiply straight across the top and bottom.
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
If an airplane is flying 225mph about how long will it take the plane to go 600 miles?
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Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Speed = distance /time; So by solving for time we get time = distance /speed. So the equation for the answer is (600 miles)/ (225 miles/hr)= 2.67 hours; Remember to round up when the last digit of concern is 5 or more.
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
Vikki is able to complete 4 SAT reading questions in 6 minutes. At this rate, how many questions can she answer in 3 1/2 hours?
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First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
First, find how many minutes are in 3 1/2 hours: 3 * 60 + 30 = 210 minutes. Then divide 210 by 6 to find how many six-minute intervals are in 210 minutes: 210/6 = 35. Since Vikki can complete 4 questions every 6 minutes, and there are 35 six-minute intervals we can multiply 4 by 35 to determine the total number of questions that she can complete.
4 * 35 = 140 problems.
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
The price of k kilograms of quartz is 50 dollars, and each kilogram makes s clocks. In terms of s and k, what is the price, in dollars, of the quartz required to make 1 clock?
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We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
We want our result to have units of "dollars" in the numerator and units of "clocks" in the denominator. To do so, put the given information into conversion ratios that cause the units of "kilogram" to cancel out, as follows: (50 dollar/k kilogram)* (1 kilogram / s clock) = 50/(ks) dollar/clock.
Since the ratio has dollars in the numerator and clocks in the denominator, it represents the dollar price per clock.
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
Minnie can run 5000 feet in 15 minutes. At this rate of speed, how long will it take her to fun 8500 feet?
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Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
Find the rate of speed. 5000ft/15 min = 333.33 ft per min
Divide distance by speed to find the time needed
8500ft/333.33ft per min = 25.5
Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?
Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?
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If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.
If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.
A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?
A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?
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We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce
66.6/0.6 = 111 ft
We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce
66.6/0.6 = 111 ft
Write as a fraction: 22%
Write as a fraction: 22%
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22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
22% = 22/100
Divide everything by 2:
22/100 = 11/50
11 is a prime number, so this is as reduced as this fraction can get.
25% of 64 is equal to 5% of what number?
25% of 64 is equal to 5% of what number?
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25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
25% of 64 is 16 (you can find this with a calculator by 0.25 * 64). Divide 16 by 0.05 (or 1/20) to get the value of the number 16 is 5% of. (Or mental math of 16 * 20)
Simplify the given fraction:
Simplify the given fraction:
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120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.
120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.
Simplify:
Simplify:
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With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:
Now we can see that the equation can all be divided by y, leaving the answer to be:
With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:
Now we can see that the equation can all be divided by y, leaving the answer to be: