A commercial bakery uses an automated mixing system to prepare large batches of dough. The… — ACT

A commercial bakery uses an automated mixing system to prepare large batches of dough. The system processes flour at a constant rate such that $F$ kilograms of flour are mixed over $m$ minutes. If the mixer consumes flour at a rate of $\frac{3}{8}$ kilogram per minute, which of the following equations correctly expresses $m$ , the total mixing time in minutes, in terms of $F$ ?

A
$m = \frac{3F}{8}$
$m = \frac{8F}{3}$ Answer
C
$m = F - \frac{3}{8}$
D
$m = \frac{3}{8F}$
E
$m = \frac{8}{3F}$

Answer

The correct equation expressing

m

in terms of

F

m = \frac{8F}{3}

The total amount of flour used is determined by multiplying the rate per minute by the number of minutes, giving the equation

F = \frac{3}{8}m

. To express

m

in terms of

F

, solve this one-step equation for

m

by dividing both sides by

\frac{3}{8}

. Dividing by

\frac{3}{8}

is mathematically equivalent to multiplying by its reciprocal,

\frac{8}{3}

. Therefore,

m = \frac{8F}{3}

Step-by-Step Solution

Set up the one-step relationship between rate, total flour, and time.

F = \frac{3}{8}m

Total flour

F

equals the rate per minute multiplied by total minutes

m

Isolate the variable

m

by dividing both sides of the equation by

\frac{3}{8}

m = \frac{F}{\frac{3}{8}}

To solve a one-step multiplication equation, apply the inverse operation (division).

Simplify the fraction division by multiplying by the reciprocal of

\frac{3}{8}

m = F \cdot \frac{8}{3} = \frac{8F}{3}

Dividing by a fraction is equivalent to multiplying by its reciprocal.

Key Concept

Solving One-Step Equations with Fractional Coefficients

Estimated Time:1m 0s

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