Practice 10 rates and proportions word problems involving unit rates, scale factors, maps, fuel efficiency, mixtures, work rates, inverse proportion, pricing, and similar figures. Use hints when needed and review a step-by-step explanation after each answer.
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These 10 problems use travel, recipes, maps, fuel, mixtures, pumps, work time, unit pricing, similar figures, and changing ratios. The central question is always the same: what quantity stays proportional, and what is the most useful unit?
The van problem gives 156 miles in 2.4 hours. Converting that comparison to one hour makes the rate easier to reuse.
| Servings | Flour |
|---|---|
| 14 | 3.5 cups |
| 1 | 0.25 cup |
| 22 | 5.5 cups |
This method is especially useful when the scale factor from the original amount to the target amount is not a whole number.
At $3 per kilogram, buying more apples increases the total cost by the same constant rate.
If individual productivity stays constant, worker-hours remain fixed.
The pump problem is a stronger proportion because two inputs change at once.
The shape stays similar, so width and height use the same scale factor.
New height = 12 × 1.75 = 21 cm.
A 5:3 blue-to-white mixture totaling 24 L contains 15 L blue and 9 L white.
Add 18 − 15 = 3 L blue. White stays unchanged.
A wrong answer often comes from choosing the wrong model before any calculation begins.