The ratio of sugar to flour is by volume. If a baker uses cups of sugar, how many cups of flour should the baker use to keep the same ratio?

Solution available with step-by-step explanation

SAT Ratios, Rates & Proportions Question 10 | Free SAT Prep | Aniko

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Question 10·Easy·Ratios, Rates, Proportional Relationships, and Units

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The ratio of sugar to flour is $2:5$ by volume. If a baker uses $3$ cups of sugar, how many cups of flour should the baker use to keep the same ratio?

For ratio questions like this, keep the order of the ratio consistent (here, sugar:flour) and set up a clear proportion: original ratio = new ratio. Put matching quantities in the same position (top or bottom) of each fraction, then solve the resulting proportion by cross-multiplying. As a quick check, make sure your final value makes sense (for example, if flour is the larger part in the ratio, its amount should be larger than the sugar amount).

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Connect the ratio to the new sugar amount

The ratio $2:5$ is sugar:flour. If sugar changes from 2 parts to 3 cups, how should flour change so the relationship stays the same?

Set up a fraction for the ratio

Write the original ratio as a fraction: sugar over flour is $\frac{2}{5}$ . Then write another fraction with 3 as the sugar amount and $x$ as the flour amount.

Use a proportion to find the missing value

Once you have $\frac{2}{5} = \frac{3}{x}$ , use cross-multiplication to solve for $x$ , then divide to find the number of cups of flour.

Desmos Guide

Use Desmos to compute the needed flour

In Desmos, type 3 * (5/2) to represent 3 cups of sugar times the flour-to-sugar ratio $\frac{5}{2}$ . The value that Desmos outputs is the number of cups of flour needed to keep the same ratio.

Step-by-step Explanation

Understand what the ratio means

The ratio $2:5$ (sugar:flour) means:

For every 2 equal-volume parts of sugar,
There are 5 equal-volume parts of flour.

So flour is the larger part, and it is always $\frac{5}{2}$ times as much as the sugar.

Set up a proportion with the new sugar amount

We are told the baker now uses 3 cups of sugar. Let $x$ be the number of cups of flour needed.

Set up the proportion so that sugar is on top and flour is on the bottom in both fractions:

\frac{2}{5} = \frac{3}{x}

This says: "2 parts sugar for 5 parts flour" is the same as "3 cups sugar for $x$ cups flour."

Solve the proportion for the flour amount

Solve the equation

\frac{2}{5} = \frac{3}{x}

by cross-multiplying:

2x = 5 \cdot 3

2x = 15

x = \frac{15}{2} = 7.5

So the baker should use 7.5 cups of flour, which corresponds to answer choice C.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation