A ratio with three parts
A made-up snack mix has groundnuts, raisins and cashews. Their ratio is 3 : 5 : 4. You have 10 cups of raisins. How much of the rest?
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- The ratio 3 : 5 : 4 is 3, 5 and 4 parts.
- You know 10 cups of raisins. That is 5 parts, so 1 part is 2 cups.
- Multiply each term by 2: 6, 10 and 8 cups.
- 6 : 10 : 8 is the same mix as 3 : 5 : 4. It is twice as big.
The rule
You need 6 cups of groundnuts and 8 cups of cashews. A ratio can have more than two terms. An ingredient is one item in the mix, like raisins. Each term is the number of parts of one ingredient.
Rule: Multiply every term by the same number. Find that number from the amount you know.
Scaling a mix changes its size but keeps its ratio.
| Ingredient | Parts | Cups |
|---|---|---|
| Groundnuts | 3 | 6 |
| Raisins | 5 | 10 |
| Cashews | 4 | 8 |
Check: 6 ÷ 3, 10 ÷ 5 and 8 ÷ 4 all give 2. Matching terms are the ones in the same place. Ratios are in proportion if matching terms divide to the same number.
Watch out!
Adding is not scaling. Raisins go from 5 to 10, which is adding 5. Adding 5 to every term gives 8 : 10 : 9. Multiplying every term by 2 gives 6 : 10 : 8.