For a given recipe, 4 cups of flour are mixed with 22 cups of sugar. How many cups of sugar should be used if 14 cups of flour are used?
Understand the Problem
The question is asking how many cups of sugar should be used if 14 cups of flour are used, assuming a constant ratio from a given recipe where 4 cups of flour are mixed with 22 cups of sugar.
Answer
77
Answer for screen readers
77 cups of sugar should be mixed with 14 cups of flour.
Steps to Solve
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Identify the Ratio The given ratio of flour to sugar from the recipe is: $$ \frac{4 \text{ cups of flour}}{22 \text{ cups of sugar}} $$
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Set up a Proportion To find the amount of sugar ($x$) needed for 14 cups of flour, we set up the proportion: $$ \frac{4}{22} = \frac{14}{x} $$
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Cross Multiply Multiply both sides to solve for $x$: $$ 4x = 22 \times 14 $$
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Calculate the Right Side Compute the product on the right: $$ 22 \times 14 = 308 $$
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Solve for x Now the equation is: $$ 4x = 308 $$
Divide both sides by 4: $$ x = \frac{308}{4} $$
- Final Calculation Calculate the final value of $x$: $$ x = 77 $$
77 cups of sugar should be mixed with 14 cups of flour.
More Information
The answer represents a direct scaling of the recipe, maintaining the same proportion of ingredients. This method can be applied to other similar problems where ingredients need to be scaled.
Tips
- Mixing up the ratios: Make sure to maintain the order of ingredients when setting up the proportion.
- Incorrectly simplifying fractions: Double-check calculations to ensure accuracy.
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