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Difficulty: MediumBasic Algebraic Expressions and One-Step Equations

A commercial printing press uses large rolls of paper for magazine production. During a morning shift, a technician uses 49\frac{4}{9} of the total mass, mm (in kilograms), of a full paper roll. If the mass of paper used during the shift is 3636 kilograms, what is the total mass mm, in kilograms, of the full paper roll?

  1. A
    9
  2. B
    16
  3. 81Answer
  4. D
    144
  5. E
    324

Answer

The total mass of the full paper roll is 81 kilograms.
To find the total mass mm, set up the equation 49m=36\frac{4}{9}m = 36. Multiplying both sides by the reciprocal 94\frac{9}{4} yields m=36×94=81m = 36 \times \frac{9}{4} = 81 kilograms.

Step-by-Step Solution

1
Set up the one-step algebraic equation based on the given word problem.
49m=36\frac{4}{9}m = 36
The problem states that 49\frac{4}{9} of the total mass mm equals 3636 kilograms.
2
Isolate the variable mm by multiplying both sides of the equation by the reciprocal of 49\frac{4}{9}, which is 94\frac{9}{4}.
m=36×94m = 36 \times \frac{9}{4}
Multiplying by the reciprocal cancels out the fraction coefficient on the left side.
3
Simplify the numerical calculation.
m=9×9=81m = 9 \times 9 = 81
Dividing 36 by 4 gives 9, and multiplying 9 by 9 results in 81.

Key Concept

Solving One-Step Linear Equations involving Fractional Coefficients
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Topics

Basic Algebraic Expressions and One-Step Equations

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