A specialty coffee roasting facility packages a batch of c pounds of dark roast coffee bea… — ACT

A specialty coffee roasting facility packages a batch of $c$ pounds of dark roast coffee beans into retail bags. Each bag is filled with exactly $1.5$ pounds of coffee. If the facility completely fills $28$ bags with no coffee left over, which of the following equations can be used to find the total weight, $c$ , in pounds, of the coffee batch?

$\frac{c}{1.5} = 28$ Answer
B
$1.5c = 28$
C
$c - 1.5 = 28$
D
$\frac{1.5}{c} = 28$
E
$c + 1.5 = 28$

Answer

The equation that can be used to find the total weight is

\frac{c}{1.5} = 28

To find the number of bags filled, the total weight of coffee (

c

) must be divided into equal parts of

1.5

pounds each. Setting this quotient equal to the total number of filled bags (

28

) gives the equation

\frac{c}{1.5} = 28

Step-by-Step Solution

Identify the given quantities and unknown variable

Total weight =

c

pounds; Weight per bag =

1.5

pounds; Total number of bags =

28

Establishing clear variable definitions is necessary before setting up an algebraic model.

Formulate the relationship between total quantity, unit rate, and total items

\frac{\text{Total Weight}}{\text{Weight per Bag}} = \text{Total Number of Bags}

Dividing a total quantity by the capacity of one container gives the total number of containers filled.

Substitute the known values and variable into the relationship formula

\frac{c}{1.5} = 28

This yields the correct one-step linear equation representing the scenario.

Key Concept

Writing one-step linear equations from word problems involving rates and equal grouping

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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