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Zorluk: OrtaInterpreting Linear Relationships in Context

A digital printing press uses paper from a large roll. The total weight WW, in pounds, of the paper remaining on the roll after mm minutes of continuous printing is given by the equation W=120−1.5mW = 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 4545 pounds?

Cevap: 50 minutes

Cevap

The correct answer is 50.
To find the number of minutes, mm, when the remaining weight is 4545 pounds, substitute W=45W = 45 into the given equation W=120−1.5mW = 120 - 1.5m. This yields the equation 45=120−1.5m45 = 120 - 1.5m. Subtracting 120120 from both sides gives −75=−1.5m-75 = -1.5m. Dividing both sides by −1.5-1.5 results in m=50m = 50. Therefore, after 5050 minutes, the remaining weight of the paper on the roll is 4545 pounds.

Adım Adım Çözüm

1
Substitute the target weight into the linear equation.
45=120−1.5m45 = 120 - 1.5m
We are given that the weight of the remaining paper, WW, is 4545 pounds, and we need to solve for the time in minutes, mm.
2
Isolate the variable term by subtracting 120120 from both sides of the equation.
−75=−1.5m-75 = -1.5m
To solve for mm, we first need to isolate the term containing the variable on one side of the equation.
3
Divide both sides by −1.5-1.5 to find the value of mm.
m=50m = 50
Dividing by the coefficient of the variable completes the isolation and gives the final value.

Anahtar Kavram

Interpreting values and solving linear equations in context

Alternatif Yöntem

Alternatively, you can determine the total weight of paper consumed: 120−45=75120 - 45 = 75 pounds. Since the paper is used at a rate of 1.51.5 pounds per minute, the time required is 751.5=50\frac{75}{1.5} = 50 minutes.
Tahmini Süre:1m 30s
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Interpreting Linear Relationships in Context

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