Question 58·Easy·Ratios, Rates, Proportional Relationships, and Units

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In a jar, the ratio of red marbles to blue marbles is $3{:}2$ . If the jar contains $18$ red marbles, how many blue marbles are in the jar?

A part-to-part ratio compares two groups in the order named. When you know one group's count, divide by that group's ratio number to find the size of one equal part, then multiply by the other group's ratio number. Don't add the ratio numbers unless you need the combined total.

Hints

Hint 1
In a part-to-part ratio, the numbers match the groups in the order named. The first ratio number belongs to red marbles. How many equal parts does the given red count fill?
Hint 2
The scale factor is the number of marbles in one equal part. Divide the red count by its ratio number, then use that same number of marbles per part for blue.

Step-by-step

Find the size of one ratio part
Step 1
Match the ratio parts to the colors
No Desmos needed. The red count divides evenly into its ratio parts. The ratio $3{:}2$ names red first, so $3$ equal parts represent red and $2$ represent blue. The $18$ counts red marbles only, not all the marbles; adding the ratio numbers would give the wrong group to divide by.
Step 2
Find the marbles in one part
The scale factor is the number of marbles in each equal part. Divide the known group's count by its own ratio number. Divide the $18$ red marbles by the $3$ red parts:
$18\div3=6.$
Step 3
Count the blue marbles
Blue has $2$ equal parts, with $6$ marbles in each. Multiply:
$2\times6=12.$
The jar has $12$ blue marbles. Choice D.

Lessons that teach this

SAT Data AnalysisBeginnerCoreReason with ratios and proportions

Question 58·Easy·Ratios, Rates, Proportional Relationships, and Units

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this