Question

carolina goes to a painthall held that charges an entrance fee of $18 and $0.08 per ball. the held 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? paintballs show calculator

Explanation:

Step1: Form the total cost expression

The entrance fee is $18$ and each paint - ball costs $0.08$. So the total cost \(C\) for \(B\) paint - balls is \(C = 18+0.08B\). The promotion is available when the total cost is $75$ or more. So the inequality is \(18 + 0.08B\geq75\).

Step2: Solve the inequality for \(B\)

Subtract $18$ from both sides of the inequality \(18 + 0.08B\geq75\):

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Divide both sides by $0.08$: \(B\geq\frac{57}{0.08}=\frac{57\times100}{8}=\frac{5700}{8}=712.5\)

Since the number of paint - balls \(B\) must be a whole number, we round up \(712.5\) to the next whole number.

Answer:

1. B. \(18 + 0.08B\geq75\)
2. \(713\) paintballs