In a jar, the ratio of red marbles to blue marbles is . If the jar contains red marbles, how many blue marbles are in the jar?
For ratio problems like this, translate the ratio into "parts" and find the scale factor from the given actual quantity. Treat as 3 red parts and 2 blue parts, divide the given number of red by 3 to find how many groups there are, then multiply the blue part (2) by that same number of groups. Alternatively, set up a proportion such as and solve for by cross-multiplying; pick whichever method feels faster and more natural for you.
Hints
Understand what means
The ratio compares red marbles to blue marbles. Think: in one "set" of marbles, how many red and how many blue are there?
Relate 18 red marbles to the ratio
If there are 3 red marbles in one set, how many such sets do you need to make 18 red marbles? What number times 3 equals 18?
Scale the blue marbles the same way
Once you know how many sets there are, multiply the number of blue marbles in one set by that number of sets.
Desmos Guide
Use Desmos to compute the proportional amount
In a Desmos expression line, type 18 * (2/3) to represent that blue marbles are as many as red. Use the numerical result shown by Desmos as the number of blue marbles.
Step-by-step Explanation
Interpret the ratio
The ratio of red to blue marbles means:
- For every 3 red marbles, there are 2 blue marbles. So one "group" in this ratio is 3 red and 2 blue.
Find how many ratio groups fit into 18 red marbles
Since there are 3 red marbles in each group and the jar has 18 red marbles, find how many groups of 3 are in 18:
So there are 6 groups of the ratio.
Use the ratio to find the number of blue marbles
Each group has 2 blue marbles, and there are 6 groups.
Multiply the number of blue marbles per group by the number of groups:
So there are blue marbles in the jar, which corresponds to answer choice D.