Problem Solving | Ratios | Level 1

SAT Math Tutorial

Problem Solving | Ratios | Level 1

Intro

This is question 1 from Lesson 3 of my book The Scholarly Unicorn’s SAT Math Advanced Guide.

Topic: Problem Solving
Subtopic: Ratios
Level: 1

Sample Problem

Question source

At an adoption center, 4 guinea pigs are selected at random from each group of 15. At this rate, how many guinea pigs will be selected in total if the adoption center has 90 guinea pigs?

Solution

Solution by setting up a ratio: (Step 1) We identify 2 key words. Let’s choose “selected” and “group.”

(Step 2) Next to the word “selected” we put the number 4 for the 4 guinea pigs that were selected from 15, followed by x for the unknown number of guinea pigs selected from the entire group of 90. Then, next to the word group, we put 15, followed by 90. Here is how it should look:

selected    4    x
   group      15    90

Note that it is important that the 15 goes under the 4 and the 90 goes under the x.

(Step 3) We now draw in 2 division symbols and an equal sign.

4/15 = x/90

(Step 4) Finally, we find x by cross multiplying and then dividing.

15x = 4 ⋅ 90

x = (4 ⋅ 90)/15 = 4 ⋅ 90/15 = 4⋅6 = 24

Notes: (1) There are always four correct ways to set up a ratio. Here are the other three possibilities:

15/4 = 90/x    x/4 = 90/15    4/x = 15/90

All four possibilities result in the equation 15x = 4 ⋅ 90 after cross multiplying.

(2) Be careful! Some setups are NOT acceptable. For example, 4/15 = 90/x is incorrect because the “selected” and “group” are mixed and matched.

* Quick ratio: 90/15 ⋅ 4 = 6 ⋅ 4 = 24.

Notes: (1) There are 90 guinea pigs in total, and there are 15 in each group. So, dividing 90 by 15 gives us the number of groups.

90/15 = 6 groups

(2) Since 4 guinea pigs are selected from each group, and there are 6 groups, the total number of guinea pigs selected is 6 ⋅ 4 = 24.

Here is a video solution for this problem:



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