An online retail store charges a flat shipping fee of 10.00 for any order, plus 5.00 per p… — ACT

An online retail store charges a flat shipping fee of $10.00$ for any order, plus $5.00$ per pound of the package's weight. A customer places an order and uses a coupon that gives them a $20\%$ discount on the total cost (the flat shipping fee plus the weight cost). If the customer's total bill after the discount is $36.00$ , what would their total bill have been, in dollars, if they had not used the coupon?

A
$30.00$
B
$38.00$
C
$42.50$
D
$43.20$
$45.00$ Cevap

Cevap

The total bill without the coupon would have been

45.00

The correct answer represents the total cost before the coupon discount. Since a

20\%

discount was applied to the entire bill, the final bill of

36.00

represents

80\%

of the original total bill. Setting up the equation

0.80T = 36.00

and dividing

36.00

0.80

yields the original total bill of

45.00

Adım Adım Çözüm

Define the variable for the original total bill and set up the equation using the discount percentage.

Let

T

represent the total bill before the coupon discount. A

20\%

discount means the customer pays

100\% - 20\% = 80\%

of the original total bill. This gives the linear equation

0.80T = 36.00

Establishing a direct relationship between the original price and the discounted price allows for a direct solution without needing to calculate the weight of the package first.

Solve the equation for

T

by dividing the discounted cost by the remaining percentage factor.

T = \frac{36.00}{0.80} = 45.00

Dividing both sides of the equation by

0.80

isolates the variable

T

, representing the original total bill in dollars.

Anahtar Kavram

Translating percentage changes and linear cost models into algebraic equations.

Alternatif Yöntem

You can also solve this by finding the weight of the package first. Setting up the equation with the weight

w

gives

0.80(10.00 + 5.00w) = 36.00

. Dividing by

0.80

simplifies the expression to

10.00 + 5.00w = 45.00

, which is the original bill. Solving further gives

5.00w = 35.00

and

w = 7

pounds. Substituting

7

back into the original cost formula yields

10.00 + 5.00(7) = 45.00

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Konular

Bu konudan daha fazla soru