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Difficulty: MediumBasic Algebraic Expressions and One-Step Equations

A municipal recycling center processes pp tons of plastic waste per hour. During a standard 14-hour operation cycle, the center processes a total of 119 tons of plastic waste. Which of the following equations represents this scenario, and what is the value of pp?

  1. 14p=11914p = 119; p=8.5p = 8.5Answer
  2. B
    p14=119\frac{p}{14} = 119; p=1,666p = 1,666
  3. C
    p+14=119p + 14 = 119; p=105p = 105
  4. D
    14p=119\frac{14}{p} = 119; p=0.118p = 0.118
  5. E
    14p=11914p = 119; p=8.25p = 8.25

Answer

The equation representing the situation is 14p=11914p = 119, which solves to p=8.5p = 8.5 tons per hour.
The total amount of plastic waste processed is determined by multiplying the rate per hour (pp) by the total number of hours (14), yielding the equation 14p=11914p = 119. Dividing both sides of this equation by 14 isolates pp, giving p=8.5p = 8.5 tons of plastic processed per hour.

Step-by-Step Solution

1
Set up the algebraic equation for total processing amount
14p=11914p = 119
Total plastic processed equals the hourly processing rate (pp) multiplied by the total hours of operation (14).
2
Solve the one-step linear equation for pp
p=11914=8.5p = \frac{119}{14} = 8.5
Divide both sides of the equation by 14 to isolate the variable pp.

Key Concept

Formulating and solving one-step linear equations from real-world rate scenarios
Estimated Time:1m 0s
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Topics

Basic Algebraic Expressions and One-Step Equations

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