A digital printing press uses paper from a large roll. The total weight W, in pounds, of t… — SAT

A digital printing press uses paper from a large roll. The total weight $W$ , in pounds, of the paper remaining on the roll after $m$ minutes of continuous printing is given by the equation $W = 120 - 1.5m$ . According to the equation, after how many minutes of continuous printing will the weight of the remaining paper on the roll be exactly $45$ pounds?

Answer: 50 minutes

Answer

The correct answer is 50.

To find the number of minutes,

m

, when the remaining weight is

45

pounds, substitute

W = 45

into the given equation

W = 120 - 1.5m

. This yields the equation

45 = 120 - 1.5m

. Subtracting

120

from both sides gives

-75 = -1.5m

. Dividing both sides by

-1.5

results in

m = 50

. Therefore, after

50

minutes, the remaining weight of the paper on the roll is

45

pounds.

Step-by-Step Solution

Substitute the target weight into the linear equation.

45 = 120 - 1.5m

We are given that the weight of the remaining paper,

W

, is

45

pounds, and we need to solve for the time in minutes,

m

Isolate the variable term by subtracting

120

from both sides of the equation.

-75 = -1.5m

To solve for

m

, we first need to isolate the term containing the variable on one side of the equation.

Divide both sides by

-1.5

to find the value of

m

m = 50

Dividing by the coefficient of the variable completes the isolation and gives the final value.

Key Concept

Interpreting values and solving linear equations in context

Alternative Method

Alternatively, you can determine the total weight of paper consumed:

120 - 45 = 75

pounds. Since the paper is used at a rate of

1.5

pounds per minute, the time required is

\frac{75}{1.5} = 50

minutes.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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