How to find proportion
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PSAT Math › How to find proportion
A survey of studio offices in a city with 14,000 employees reveals that there are, on average, 12.5 employees per office. If there have been a cumulative total of 3,400 printers sold to the offices of the city, what is the best estimate of the average number of printers per office?
0.33
0.77
1.2
3.0
4.1
Explanation
The best estimate would be to simply divide the number of printers by the number of offices. However, they only gave us the average number of employees per office, thus to find the number of offices we divide:
14,000 (people)/12.5 (per office) = 14,000/12.5 = 1,120 offices
We already know the number of printers available total, thus again divide
3,400 (printers)/1,120 (offices) = 3.04, or 3.0 printers per office as the best estimate.
If 1015 meters = 1 petameter and 1018 meters = 1 exameter, how many petameters are equal to 1 exameter?
0.01
0.1
10000
100
1000
Explanation
The problem gives us two conversion ratios, which are (1018 meters/ 1 exameter) and (1 petameter/ 1015 meters).
We convert 1 exameter into petameters by multiplying 1 exameter by the conversion ratios so that all units other than petameters cancel out: 1 exameter * (1018 meters/ 1 exameter) * (1 petameter/ 1015 meters). Therefore one exameter is 1018/1015 petameters. Finally, when dividing terms with common bases, we subtract the exponents, so our result is 1018/1015 = 103 = 1000.
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?
(cq )/(10 )
(c )/(10q )
(10c )/(q )
10cq
Explanation
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.
John is 35 years old, 5 years older than his brother Bob and 20 years younger than his father Jack. How old was Jack when Bob was born?
20
28
35
25
5
Explanation
If John is 35, that means currently Jack is 55 and Bob is 30. 55 – 30 = 25 years old when Bob was born.
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?
5
6
8
9
12
Explanation
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
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)?
$2855.47
$1060.60
$1794.87
$3181.81
$2692.31
Explanation
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
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?
2
4
5
6
8
Explanation
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.
Six is to thirteen-and-a-half as seventeen is to what?
None of the other answers are correct.
Explanation
Let us express this as an algebraic expression:
We can cross multiply:
If Shaquille O'Neal is 7 feet tall and casts a shadow 5 feet long. At the same time of day, how long would the shadow be from a 49-foot tall house?
35
25
45
15
55
Explanation
The question is about similar triangles. The height of the two objects would correspond with each other and the shadows would correspond with each other. As with many geometry problems, it is helpful if you draw a diagram. Set up a proportion for each so the height of Shaquille O'Neal to the height of the house then his shadow to the shadow of the house.
7/49 = 5/x
Solve for x by cross-multiplying:
5 * 49 = 7x
x = 35
A recipe calls for a ratio of 
Explanation
We can set up a ratio of 
