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Solve ratio word problems

Ratio word problems require interpreting a comparison between quantities as a multiplicative relationship, distinguishing part-to-part from part-to-whole ratios and identifying what each number represents. Solutions determine unknown amounts, totals, or scale factors by generating equivalent ratios and using tables, double number lines, bar models, or equations, rather than applying additive differences. The scope is familiar contexts with positive whole-number or simple rational quantities, not complex compound ratios, formal proportional functions, or proof-based generalizations.

Detailed Explanation: Solve ratio word problems

A ratio compares quantities by showing how many equal-sized parts each quantity has. For example, a ratio of 2:32:3 means:

  • the first quantity has 22 parts;
  • the second quantity has 33 parts.

The numbers are not an additive difference. They show a multiplicative relationship.

Example:
The ratio of almonds to raisins in a trail mix is 2:32:3. If there are 1515 cups of raisins, how many cups of trail mix are there altogether?

First, match each number in the ratio to its quantity:

almonds:raisins=2:3\text{almonds}:\text{raisins}=2:3

The 33 parts of raisins equal 1515 cups. Find the amount in 11 part:

15÷3=515\div 3=5

So each part represents 55 cups. The almonds have 22 parts:

2×5=102\times 5=10

There are 1010 cups of almonds. Add the two quantities to find the total:

10+15=2510+15=25 25 cups of trail mix\boxed{25\text{ cups of trail mix}}

Check the ratio:

10:15=2:310:15=2:3

So the answer matches the original ratio.

Learn by doing: Solve ratio word problems

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Ratios - Equivalent, Expanding Recipes with Non-Integer Multiples - Whole Numbers


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