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Difficulty: HardBasic Algebraic Expressions and One-Step Equations

A school club is raising money by selling rolls of wrapping paper. The club keeps 40%40\% of the total sales revenue as profit. If the club made a profit of $220\$220 from selling rr rolls of wrapping paper that cost $10\$10 each, which of the following equations can be used to find rr?

  1. A
    0.40r=2200.40r = 220
  2. B
    10r=22010r = 220
  3. 4r=2204r = 220Answer
  4. D
    10r+0.40=22010r + 0.40 = 220
  5. E
    25r=22025r = 220

Answer

The equation expressing the profit is the profit per roll multiplied by the number of rolls, which yields 4r=2204r = 220.
To find the correct equation, we calculate the profit per roll of wrapping paper. Since each roll is sold for $10\$10 and the club keeps 40%40\% of the revenue as profit, the profit per roll is 0.40×10=40.40 \times 10 = 4 dollars. For rr rolls sold, the total profit is 4r4r dollars. Setting this equal to the given profit of $220\$220 yields the equation 4r=2204r = 220.

Step-by-Step Solution

1
Determine the expression for the total sales revenue.
The total revenue is 10r10r dollars.
Each of the rr rolls of wrapping paper is sold for $10\$10.
2
Express the profit as a fraction of the total sales revenue.
The profit is 0.40×10r=4r0.40 \times 10r = 4r dollars.
The club keeps 40%40\% (0.400.40) of the total revenue as profit.
3
Set the profit expression equal to the actual profit made to form the equation.
4r=2204r = 220
The total profit made by the club is given as $220\$220.

Key Concept

Translating a multi-step real-world scenario into a one-step linear equation

Alternative Method

Find the profit per roll first: 40%40\% of $10\$10 is $4\$4. Thus, the profit for rr rolls is 4r4r. Since the total profit is $220\$220, the equation is 4r=2204r = 220.
Estimated Time:1m 30s
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Topics

Basic Algebraic Expressions and One-Step Equations

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