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A high school coach needs to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 and needs to determine how much he can spend per pair of shorts. Write and solve an inequality to determine the maximum price for each pair of shorts. What does the solution represent?

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Answer:

15x < 200; x < 13.33; the maximum price for a pair of shorts

Step-by-step explanation:

1. Set up the inequality

Let x = price of a pair of shorts. Then

 15x = price of shorts for the team

You have one condition:

15x < 200

2. Solve the inequality

[tex]\begin{array}{rcl}15x & < & 200\\\\x & < & \dfrac{200}{15}\\\\x & < & \mathbf{13.333}\\\end{array}[/tex]

3. Meaning of solution

The solution represents the maximum price the coach can pay for a pair of shorts.

If the coach pays $13.33 per pair, the total cost for the team will be $199.95, and the condition is satisfied.

Answer: The coach may spend up to $13.33 per pair of shorts.

Step-by-step explanation:

Hi, to answer this question we have to write an inequality with the information given:

  • Number of shorts: 15 (for 15 members)
  • Budget: $200

So, we have to multiply the number of shorts by the price of each one, we will represent the price with the variable "x".(15x)

That cost must be equal or less to 200.

Mathematically speaking

15 x ≤ 200

Solving for x

x ≤200/15

x ≤ 13.33

This solution represents that the coach may spend up to $13.33 per pair of shorts.

Feel free to ask for more if needed or if you did not understand something.