A commercial printing press uses large rolls of paper for magazine production. During a mo… — ACT

A commercial printing press uses large rolls of paper for magazine production. During a morning shift, a technician uses $\frac{4}{9}$ of the total mass, $m$ (in kilograms), of a full paper roll. If the mass of paper used during the shift is $36$ kilograms, what is the total mass $m$ , in kilograms, of the full paper roll?

A
9
B
16
81Cevap
D
144
E
324

Cevap

The total mass of the full paper roll is 81 kilograms.

To find the total mass

m

, set up the equation

\frac{4}{9}m = 36

. Multiplying both sides by the reciprocal

\frac{9}{4}

yields

m = 36 \times \frac{9}{4} = 81

kilograms.

Adım Adım Çözüm

Set up the one-step algebraic equation based on the given word problem.

\frac{4}{9}m = 36

The problem states that

\frac{4}{9}

of the total mass

m

equals

36

kilograms.

Isolate the variable

m

by multiplying both sides of the equation by the reciprocal of

\frac{4}{9}

, which is

\frac{9}{4}

m = 36 \times \frac{9}{4}

Multiplying by the reciprocal cancels out the fraction coefficient on the left side.

Simplify the numerical calculation.

m = 9 \times 9 = 81

Dividing 36 by 4 gives 9, and multiplying 9 by 9 results in 81.

Anahtar Kavram

Solving One-Step Linear Equations involving Fractional Coefficients

Soru

Cevap

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Anahtar Kavram

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Konular

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