Solve part-to-part ratio problems

Part-to-part ratio problems involve interpreting a ratio such as 2:3 as two equal-sized units of one quantity for every three equal-sized units of another, rather than as a fraction of the whole. Given a total, one part, or a related quantity, the learner finds the value of one ratio unit and scales both parts consistently, using equivalent ratios, tables, bar models, or equations. The scope is familiar numerical contexts, not compound ratios, algebraic generalization, or advanced proportional cases.

Detailed Explanation: Solve part-to-part ratio problems

A part-to-part ratio compares two quantities by counting equal-sized units.

For example, suppose the ratio of red marbles to blue marbles is

2:3

This means:

Red marbles: $2$ equal-sized units
Blue marbles: $3$ equal-sized units

Example

There are $25$ marbles altogether. The ratio of red marbles to blue marbles is $2:3$ . How many marbles of each color are there?

Step 1: Find the total number of ratio units.

2+3=5\text{ units}

Step 2: Find the value of one unit.

The $5$ units represent all $25$ marbles:

25\div 5=5

So, each ratio unit represents $5$ marbles.

Step 3: Find each part.

Red marbles:

2\times 5=10

Blue marbles:

3\times 5=15

Answer: There are 10 red marbles and 15 blue marbles.

Check the answer:

10+15=25

and

10:15=2:3

So the ratio and the total both match.

Learn by doing: Solve part-to-part ratio problems

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Ratios - Calculate Total from Item Ratio

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