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Difficulty: EasySolving Linear Equations

The weight of Box A is 1.51.5 pounds more than 23\frac{2}{3} of the weight of Box B. If the weight of Box A is 13.513.5 pounds, what is the weight of Box B, in pounds?

  1. A
    8
  2. B
    10.5
  3. C
    13.5
  4. 18Answer
  5. E
    22.5

Answer

The weight of Box B is 18 pounds.
The weight of 18 pounds is correct. Translating the word problem yields the linear equation A=23B+1.5A = \frac{2}{3}B + 1.5. Substituting the weight of Box A (13.513.5) gives 13.5=23B+1.513.5 = \frac{2}{3}B + 1.5. Subtracting 1.51.5 from both sides results in 12=23B12 = \frac{2}{3}B. Multiplying both sides by the reciprocal 32\frac{3}{2} isolates BB, giving B=12×32=18B = 12 \times \frac{3}{2} = 18.

Step-by-Step Solution

1
Translate the verbal description into an algebraic equation.
Let AA represent the weight of Box A and BB represent the weight of Box B. The description translates to the equation: A=23B+1.5A = \frac{2}{3}B + 1.5.
This establishes the mathematical relationship between the weights of the two boxes.
2
Substitute the given value for Box A into the equation and isolate the term containing the variable B.
13.5=23B+1.5  ⟹  12=23B13.5 = \frac{2}{3}B + 1.5 \implies 12 = \frac{2}{3}B.
Substituting 13.513.5 for AA and subtracting 1.51.5 from both sides simplifies the equation to isolate the fraction term.
3
Solve for B by multiplying both sides of the equation by the reciprocal of the coefficient.
B=12×32=18B = 12 \times \frac{3}{2} = 18.
Multiplying by the reciprocal 32\frac{3}{2} isolates BB to find its value.

Key Concept

Translating real-world descriptions into multi-step linear equations and solving them using inverse operations.
Estimated Time:1m 0s
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Topics

Solving Linear Equations

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