A baker prepares a batch of sourdough bread using flour, water, and yeast. The correct rec… — ACT

A baker prepares a batch of sourdough bread using flour, water, and yeast. The correct recipe requires a flour-to-water ratio of $5:3$ by weight, and a water-to-yeast ratio of $8:1$ by weight. However, when mixing the ingredients, the baker accidentally uses a flour-to-water ratio of $3:2$ by weight while keeping the correct water-to-yeast ratio of $8:1$ . If the baker used exactly $12$ ounces of yeast in this incorrect batch, how many ounces of flour must be added to the mixture to restore the correct flour-to-water ratio of $5:3$ ?

$16$ Answer
B
$32$
C
$48$
D
$96$
E
$160$

Answer

The baker must add

16

ounces of flour.

First, use the correct water-to-yeast ratio of

8:1

to find the weight of water in the batch. Since

12

ounces of yeast were used, the weight of the water is

12 \times 8 = 96

ounces. Next, determine the initial weight of flour using the incorrect flour-to-water ratio of

3:2

. The initial weight of flour is

96 \times \frac{3}{2} = 144

ounces. To restore the correct flour-to-water ratio of

5:3

, find the target weight of flour for

96

ounces of water, which is

96 \times \frac{5}{3} = 160

ounces. Finally, subtract the initial weight of flour from the target weight of flour to find the additional flour needed:

160 - 144 = 16

ounces.

Step-by-Step Solution

Find the weight of water using the correct water-to-yeast ratio.

The water weight is

12 \text{ oz} \times 8 = 96 \text{ ounces}

The water-to-yeast ratio is

8:1

by weight, and

12

ounces of yeast were used.

Find the initial weight of flour in the incorrect batch.

The initial flour weight is

96 \text{ oz} \times \frac{3}{2} = 144 \text{ ounces}

The incorrect batch was mixed with a flour-to-water ratio of

3:2

by weight.

Find the target weight of flour required for the correct ratio.

The target flour weight is

96 \text{ oz} \times \frac{5}{3} = 160 \text{ ounces}

The correct recipe requires a flour-to-water ratio of

5:3

by weight.

Calculate the weight of additional flour needed.

The additional flour needed is

160 \text{ oz} - 144 \text{ oz} = 16 \text{ ounces}

Subtracting the initial flour weight from the target flour weight gives the amount to be added.

Key Concept

Ratios and Proportions

Question

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Step-by-Step Solution

Key Concept

Common Mistakes

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