Question

carolina goes to a paintball field that charges an entrance fee of $18 and $0.08 per ball. the field has a promotion that says, \get $10 off if you spend $75 or more!\ carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion. let b represent the number of paintballs that carolina buys. 1) which inequality describes this scenario? choose 1 answer: a 18 + 0.08b < 75 b 18 + 0.08b ≥ 75 c 18 + 0.08b < 10 d 18 + 0.08b ≥ 10 2) what is the smallest number of paintballs that carolina can buy along with the entrance fee to get the promotion?

Explanation:

Step1: Analyze the cost - promotion relationship

The entrance fee is $18$, and each paint - ball costs $0.08$ dollars. The promotion is to get $10$ dollars off if the total cost is $75$ or more. The total cost is the sum of the entrance fee and the cost of paint - balls, which is $18 + 0.08B$. We want to find when she gets the promotion, i.e., when the total cost is $75$ or more.
So the inequality is $18+0.08B\geq75$.

Step2: Solve the second - part of the problem

We have the inequality $18 + 0.08B\geq75$. First, subtract $18$ from both sides of the inequality:
$0.08B\geq75 - 18$.
$0.08B\geq57$. Then divide both sides by $0.08$: $B\geq\frac{57}{0.08}=712.5$. Since the number of paint - balls must be a whole number, the smallest number of paint - balls is $713$.

Answer:

1. C. $18 + 0.08B\geq75$
2. $713$