Question

in 5 - 6, choose the inequality that could be used to solve each problem.

1. a new van is priced at $19,500. if the buyer chooses to finance, they will pay $5,000 as a down - payment and $375 per month. after how many months will the buyer have paid more than $10,000 toward the van?

a. 19,500 - 5000x>10,000
b. 5,000 + 375x>10,000
c. 5,000x + 375>10,000
d. 19,500 - 375x<10,000

1. a trampoline park charges $5.50 per hour for kids and a flat $3 admission fee for parents. mrs. bernard would like to take her son and spend no more than $20 at the trampoline park. how many hours will her son be able to jump?

a. 5.50x + 3>20
b. 5.50x + 3≤20
c. 3x + 5.50<20
d. 3x + 5.50≤20

Explanation:

Step1: Analyze trampoline - park problem

Let $x$ be the number of hours. The cost for the child is $5.50x$ (cost per - hour times number of hours) and the parent's admission is $3$. The total cost should be no more than $20$. So the inequality is $5.50x + 3\leq20$.

Step2: Analyze van - buying problem

The van price is $19500$, the down - payment is $5000$, and the monthly payment is $375$. Let $x$ be the number of months. The amount paid after $x$ months is $5000+375x$, and we want to find when the amount paid is more than the down - payment plus the remaining cost. The inequality is $5000 + 375x>10000$.

For the trampoline - park problem, the correct inequality is $5.50x + 3\leq20$; for the van - buying problem, the correct inequality is $5000 + 375x>10000$.

Answer:

For the trampoline - park problem: B. $5.50x + 3\leq20$
For the van - buying problem: C. $5000x+375 > 10000$ (There is a small error in the options, it should be $5000 + 375x>10000$, but among the given options, C is the closest in form)