Question

a school basketball team needs to raise at least $300. they already raised $55. the team is planning a car wash where they will make $10 per car. they want to know how many cars they need to wash. let c be the number of cars the team washes. 55 + 10c ≥ 300 c ≥ 24.5 decide whether the team can wash each number of cars to raise enough money. yes no 24 cars 24.5 cars 25 cars which graph best represents the number of cars the team needs to wash?

Explanation:

Step1: Analyze the inequality solution

We have the inequality \(55 + 10c\geq300\). Solving for \(c\):

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Since the number of cars \(c\) must be a whole number (you can't wash a fraction of a car), \(c\geq25\) (because \(24.5\) is not a whole - number of cars, and \(24\) cars would give \(55+10\times24=55 + 240=295<300\))

Step2: Check each number of cars

• For \(24\) cars: \(55+10\times24=55 + 240 = 295<300\), so the answer is No.
• For \(24.5\) cars: You can't wash half a car in a practical sense, so this is not a valid number of cars for the context.
• For \(25\) cars: \(55+10\times25=55 + 250=305\geq300\), so the answer is Yes.

Step3: Analyze the graph

The inequality \(c\geq25\) (since \(c\) is a whole number) is represented on a number - line graph with a closed circle at \(25\) (because \(c = 25\) is included in the solution set) and an arrow to the right (indicating all values greater than \(25\)).

Answer:

• For \(24\) cars: No
• For \(24.5\) cars: No
• For \(25\) cars: Yes
• The correct graph is the one with a closed circle at \(25\) and an arrow to the right.