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Difficulty: MediumSolving Linear Equations

A marketing firm charges a flat setup fee of 160160 plus 3.203.20 for each promotional brochure printed. For a large order, the firm applies a 15%15\% discount to the total cost (the sum of the setup fee and the printing cost). If the final discounted bill is 680680, how many brochures were printed?

  1. A
    170
  2. B
    20
  3. 200Answer
  4. D
    250
  5. E
    300

Answer

200
The correct answer of 200 brochures is found by formulating the equation 0.85(160+3.2b)=6800.85(160 + 3.2b) = 680. Dividing both sides by 0.850.85 yields 160+3.2b=800160 + 3.2b = 800. Subtracting 160160 gives 3.2b=6403.2b = 640, and dividing by 3.23.2 results in b=200b = 200.

Step-by-Step Solution

1
Translate the word problem into a linear equation where bb represents the number of brochures. The total cost before discount is 160+3.2b160 + 3.2b. Applying a 15%15\% discount means paying 85%85\% of this total.
0.85(160+3.2b)=6800.85(160 + 3.2b) = 680
This sets up the relationship between the total discounted bill and the number of brochures.
2
Divide both sides of the equation by 0.850.85 to isolate the expression within parentheses.
160+3.2b=800160 + 3.2b = 800
Dividing by 0.850.85 simplifies the equation by calculating the total cost before the discount was applied.
3
Subtract 160160 from both sides to isolate the term containing the variable bb.
3.2b=6403.2b = 640
Subtracting the flat setup fee isolates the printing cost of the brochures.
4
Divide both sides by 3.23.2 to solve for bb.
b=200b = 200
Dividing by the per-brochure printing cost yields the total number of brochures printed.

Key Concept

Solving multi-step linear equations involving percentage discounts and decimal coefficients.

Alternative Method

Instead of dividing by 0.850.85 first, you can distribute 0.850.85 to both terms inside the parentheses to get 136+2.72b=680136 + 2.72b = 680. Subtract 136136 from both sides to get 2.72b=5442.72b = 544, then divide by 2.722.72 to find b=200b = 200.
Estimated Time:1m 30s
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Topics

Solving Linear Equations

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