Question

at a trampoline park, the individual rate for admission is $6 per person plus $2 per person for socks. the group rate is a $25 rental fee plus $8 per person, with socks included. when will the group rate be the same as the individual rate? let p = people. which equation represents this situation? 10 people 6 people the group rate always equals the individual rate. never, there is no amount of people where the group rate will be the same as the individual rate.

Explanation:

Step1: Define individual rate

Individual cost per person: $\$6 + \$2 = \$8$, so total individual rate: $8p$

Step2: Define group rate

Group rate has fixed fee + per-person cost: $25 + 8p$

Step3: Set rates equal, solve

$$8p = 25 + 8p$$
Subtract $8p$ from both sides: $0 = 25$
This is a false statement, so no solution exists.

Answer:

Never, there is no amount of people where the group rate will be the same as the individual rate.