Question

A museum reduced the price of its family membership by 20%. Jamel also has a coupon for $5 off a family membership. The museum first applies the coupon, then takes 20% off the reduced price. Jamel pays $64 for his family’s membership.

Answer 1

To find the original price of the family membership at the museum, we can set up the following equations based on the problem description:

1. Let \( x \) be the original price of the family membership.
2. Jamel uses a $5 coupon first, so the price after the coupon is applied becomes \( x - 5 \).
3. Then, the museum applies a 20% discount. The amount after applying this discount can be calculated as follows:

\[
\text{Discounted Price} = (x - 5) - 0.20 \times (x - 5) = (x - 5) \times (1 - 0.20) = (x - 5) \times 0.80
\]

4. Jamel pays $64 for the membership, so we can set up the equation:

\[
(x - 5) \times 0.80 = 64
\]

5. Now we will solve for \( x \):

\[
x - 5 = \frac{64}{0.80}
\]

Calculating the right side:

\[
\frac{64}{0.80} = 80
\]

Thus, we have:

\[
x - 5 = 80
\]

Adding 5 to both sides gives:

\[
x = 80 + 5 = 85
\]

6. Therefore, the original price of the family membership is \( \boxed{85} \).

### Verification:

To verify, we'll check the calculations:

- Original price: $85
- After applying the coupon:
\[
85 - 5 = 80
\]
- After applying the 20% discount:
\[
80 \times 0.80 = 64
\]

This confirms that Jamel pays $64, verifying that the original price of the family membership is indeed \( \boxed{85} \).