A commercial bakery uses an industrial mixer that processes specialty flour at a constant … — ACT

A commercial bakery uses an industrial mixer that processes specialty flour at a constant rate. The mixer consumes $\frac{4}{7}$ of a full bag of flour in $12$ minutes. The equation $\frac{4}{7}b = 12$ represents this situation, where $b$ is the time, in minutes, it takes to process one full bag of flour. What is the value of $b$ ?

A
$\frac{48}{7}$
$21$ Answer
C
$28$
D
$48$
E
$\frac{3}{7}$

Answer

The total time required to process one full bag of flour is 21 minutes.

To solve the one-step equation

\frac{4}{7}b = 12

, isolate

b

by multiplying both sides of the equation by the reciprocal of

\frac{4}{7}

, which is

\frac{7}{4}

. Computing

12 \times \frac{7}{4}

yields

\frac{84}{4} = 21

. Therefore, 21 minutes is the correct answer.

Step-by-Step Solution

Identify the given one-step equation

\frac{4}{7}b = 12

The equation models the relationship between the fraction of the bag used and the time taken.

Isolate the variable

b

by multiplying both sides by the reciprocal of

\frac{4}{7}

b = 12 \times \frac{7}{4}

Multiplying by the reciprocal undoes multiplication by a fraction.

Simplify the numerical calculation

b = \frac{12 \times 7}{4} = 3 \times 7 = 21

Dividing 12 by 4 yields 3, and multiplying 3 by 7 gives 21.

Key Concept

Solving One-Step Linear Equations with Fractional Coefficients

Estimated Time:1m 0s

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