A commercial bakery makes a standard pastry dough using a ratio of 7 parts flour to 3 part… — Armed Services Vocational Aptitude Battery (ASVAB)

A commercial bakery makes a standard pastry dough using a ratio of $7$ parts flour to $3$ parts butter by weight. If a daily batch requires $42$ pounds of flour, how many pounds of butter are needed?

$18$ Answer
B
$60$
C
$98$
D
$126$

Answer

18

The ratio of flour to butter is given as

7:3

. Setting up a direct proportion where

x

is the pounds of butter needed:

\frac{7}{3} = \frac{42}{x}

. Cross-multiplying gives

7x = 126

. Solving for

x

yields

x = 18

pounds of butter.

Step-by-Step Solution

Identify the given ratio and the known quantity.

The ratio of flour to butter is

7:3

. The known quantity of flour is

42

pounds.

To set up a proportion, we must align the correct parts of the ratio with the real-world amounts.

Set up a direct proportion equation.

\frac{7}{3} = \frac{42}{x}

The ratio of parts must equal the ratio of the actual weights.

Solve for the unknown value

x

7x = 3 \times 42 \rightarrow 7x = 126 \rightarrow x = 18

Cross-multiplying and dividing isolates the variable to find the required pounds of butter.

Key Concept

Direct Proportions

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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