Question

41. Kylie is buying a new computer. She has a coupon that will reduce the price of any computer in the

store by $50. The store charges 5% sales tax on the reduced price. Which inequality represents all

of the possible original prices, p, of computers that will cost less than $800 after the coupon and tax

are applied?

햠 1.05p , 747.5

햡 1.05p , 750

햢 1.05p , 850

햣 1.05p , 852.5

Answer 1

To find the inequality that represents all the possible original prices \( p \) of computers that will cost less than $800 after applying the coupon and sales tax, we start with the following steps:

1. **Reduce the price with the coupon**: The coupon reduces the original price \( p \) by $50, so the price after the coupon is \( p - 50 \).

2. **Apply sales tax**: The store charges a 5% sales tax, which means the final price after tax can be calculated as follows:
\[
\text{Final price} = (p - 50) \times 1.05
\]

3. **Set up the inequality**: We want this final price to be less than $800:
\[
(p - 50) \times 1.05 < 800
\]

4. **Distribute 1.05**:
\[
1.05p - 52.5 < 800
\]

5. **Add 52.5 to both sides**:
\[
1.05p < 852.5
\]

6. **Divide each side by 1.05 to isolate \( p \)**:
\[
p < \frac{852.5}{1.05} \approx 812.38
\]

Now, interpreting this, it gives us the upper limit of the original price.

The two options are:
- 1.05p < 852.5
- 1.05p < 850

Based on what we derived, the final price comparison shows that the solution corresponds to \( 1.05p < 852.5 \).

Thus, the correct inequality is:

**햣 1.05p < 852.5**.