Question

Ryan goes to a store and buys an item that costs xx dollars. He has a coupon for 5% off, and then a 7% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Ryan paid at the register.

Answer 1

To find the total amount that Ryan paid at the register, we can follow these steps:

1. **Calculate the discount using the coupon**:
The discount is 5% of \( x \). Therefore, the discount amount is:
\[
0.05x
\]
After applying the discount, the price before tax becomes:
\[
x - 0.05x = 0.95x
\]

2. **Calculate the tax on the discounted price**:
The tax is 7% of the discounted price, which is \( 0.95x \). The tax amount is:
\[
0.07 \times 0.95x = 0.0665x
\]

3. **Calculate the total amount paid**:
The total amount Ryan pays at the register includes the discounted price plus the tax:
\[
0.95x + 0.0665x
\]
Combining the two expressions gives:
\[
(0.95 + 0.0665)x = 1.0165x
\]

Thus, the expression that represents the total amount that Ryan paid at the register is:
\[
\boxed{1.0165x}
\]