A marketing firm charges a flat setup fee of 160 plus 3.20 for each promotional brochure p… — ACT

A marketing firm charges a flat setup fee of $160$ plus $3.20$ for each promotional brochure printed. For a large order, the firm applies a $15\%$ discount to the total cost (the sum of the setup fee and the printing cost). If the final discounted bill is $680$ , how many brochures were printed?

A
170
B
20
200Cevap
D
250
E
300

Cevap

200

The correct answer of 200 brochures is found by formulating the equation

0.85(160 + 3.2b) = 680

. Dividing both sides by

0.85

yields

160 + 3.2b = 800

. Subtracting

160

gives

3.2b = 640

, and dividing by

3.2

results in

b = 200

Adım Adım Çözüm

Translate the word problem into a linear equation where

b

represents the number of brochures. The total cost before discount is

160 + 3.2b

. Applying a

15\%

discount means paying

85\%

of this total.

0.85(160 + 3.2b) = 680

This sets up the relationship between the total discounted bill and the number of brochures.

Divide both sides of the equation by

0.85

to isolate the expression within parentheses.

160 + 3.2b = 800

Dividing by

0.85

simplifies the equation by calculating the total cost before the discount was applied.

Subtract

160

from both sides to isolate the term containing the variable

b

3.2b = 640

Subtracting the flat setup fee isolates the printing cost of the brochures.

Divide both sides by

3.2

to solve for

b

b = 200

Dividing by the per-brochure printing cost yields the total number of brochures printed.

Anahtar Kavram

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

Alternatif Yöntem

Instead of dividing by

0.85

first, you can distribute

0.85

to both terms inside the parentheses to get

136 + 2.72b = 680

. Subtract

136

from both sides to get

2.72b = 544

, then divide by

2.72

to find

b = 200

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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Alternatif Yöntem

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