Question

1. model with mathematics arlene buys a phone case and charging cord for 15% off. the original cost of the phone case is $18. her total discount is $4.20. write and solve an equation to find the original price of the charging cord.

Explanation:

Step1: Define the variable

Let \( x \) be the original price of the charging cord (in dollars). The original price of the phone case is $18, so the total original price of the phone case and the charging cord is \( 18 + x \) dollars.

Step2: Set up the equation

The discount is 15% of the total original price, and this discount is $4.20. The formula for the discount is \( \text{Discount} = \text{Rate} \times \text{Original Price} \). So we can write the equation:
\( 0.15(18 + x) = 4.20 \)

Step3: Solve the equation

First, divide both sides of the equation by 0.15:
\( \frac{0.15(18 + x)}{0.15} = \frac{4.20}{0.15} \)
\( 18 + x = 28 \)
Then, subtract 18 from both sides:
\( 18 + x - 18 = 28 - 18 \)
\( x = 10 \)

Answer:

The original price of the charging cord is \(\$10\).