Question 15

The price of the more expensive pan is $15.95.

To determine the price of the more expensive pan, we set up a system of equations based on the information provided. Let the price of the less expensive pan be \( x \). Then, the price of the more expensive pan can be expressed as \( x + 5.96 \). The total price of both pans is given as $25.94, leading to the equation \( x + (x + 5.96) = 25.94 \).

A) $9.99

This option is incorrect. If we assume the less expensive pan costs $9.99, then the more expensive pan would cost $9.99 + $5.96 = $15.95, resulting in a total of $9.99 + $15.95 = $25.94. While this total matches, it does not directly determine that $9.99 is the price of the less expensive pan since we need to confirm both prices.

B) $12.97

This option is incorrect. Assuming the less expensive pan costs $12.97, the more expensive pan would be $12.97 + $5.96 = $18.93. The combined total would then equal $12.97 + $18.93 = $31.90, which exceeds the total of $25.94.

C) $14.05

This option is incorrect. If the less expensive pan is priced at $14.05, the more expensive pan would then be $14.05 + $5.96 = $20.01. The total would be $14.05 + $20.01 = $34.06, which again is greater than the total of $25.94.

D) $15.95

This option is correct. If we let the less expensive pan cost \( x \), then \( x + 5.96 = 15.95 \) implies \( x = 15.95 - 5.96 = 9.99 \). The total price would be $9.99 + $15.95 = $25.94, which matches the given total.

E) $16.98

This option is incorrect. If the less expensive pan costs $16.98, the more expensive pan would be $16.98 + $5.96 = $22.94. The total would then be $16.98 + $22.94 = $39.92, which is well above $25.94.

Conclusion

The price of the more expensive pan is definitively $15.95, as it satisfies both the individual price comparison and the total price requirement of $25.94. All other options fail to meet either the price difference or the overall total, confirming that D is the only correct choice.