PSAT Math : How to find proportion
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Example Questions
Example Question #61 : Proportion / Ratio / Rate
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?
2
4
1
3
5
2
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.
Example Question #551 : Arithmetic
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?
1.2
0.77
3.0
0.33
4.1
3.0
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.
Example Question #11 : How To Find Proportion
A factory makes six widgets in a batch that takes 24 minutes to complete. How long does it take to make 57 widgets?
3 hours
3 hours, 5 minutes
4 hours
3 hours, 45 minutes
3 hours, 30 minutes
4 hours
We have here a basic ratio:
6/24 = 57/x
Solving for x, we get: 6x = 24 * 57; 6x = 1368; x = 228
Now, we must be very careful here, however. Is 228 an even multiple of 24? 228/24 = 9.5. That means that we would have to do 9.5 batches. The question indicates that these are batched in groups of 6; therefore, we have to run 10 batches to get our amount. That would be 240 minutes or 4 hours.
Example Question #11 : How To Find Proportion
Kendall can run 26 miles in 4 hours and 20 minutes. At this rate how long would it take him to run 100 miles?
16 hours and 40 minutes
18 hours and 35 minutes
15 hours and 50 minutes
12 hours and 20 minutes
10 hours and 55 minutes
16 hours and 40 minutes
Set up a proportion and conver 4 hours and 20 minutes into just minutes for now,
so 26/260 = 100/X
Solve for X = 1000 minutes
1000/60 = 16 hours and 40 minutes
Example Question #12 : How To Find Proportion
A recipe calls for a ratio of 
We can set up a ratio of 
Example Question #11 : How To Find Proportion
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.
Example Question #17 : How To Find Proportion
Six is to thirteen-and-a-half as seventeen is to what?
None of the other answers are correct.
Let us express this as an algebraic expression:
We can cross multiply:
Example Question #13 : How To Find Proportion
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?
1/10
19/80
16/85
7/40
1/8
16/85
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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