A coach of a soccer team orders shin guards for the players on his team. Each pair of shin guards costs $8.95. The shipping fee for the entire order is $10. The total cost of the c... A coach of a soccer team orders shin guards for the players on his team. Each pair of shin guards costs $8.95. The shipping fee for the entire order is $10. The total cost of the coach's order is less than $115. Which inequality can be used to determine the greatest number of shin guards, s, the coach orders?
Understand the Problem
The question is asking for the correct inequality that represents the total cost of ordering shin guards, taking into account the price per pair, shipping fees, and a maximum total cost. The goal is to determine which inequality can be used to find the maximum number of shin guards the coach can order without exceeding $115.
Answer
The correct inequality is: $$ 8.95s + 10 < 115 $$
Answer for screen readers
The inequality that represents the maximum number of shin guards the coach can order is: $$ 8.95s + 10 < 115 $$
Steps to Solve
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Identify the components of the total cost
Each pair of shin guards costs $8.95, and there is a shipping fee of $10. Therefore, the total cost $C$ of ordering $s$ pairs of shin guards can be expressed as: $$ C = 8.95s + 10 $$
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Set up the inequality for the total cost
According to the problem, the total cost must be less than $115. Thus, we can set up the inequality: $$ 8.95s + 10 < 115 $$
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Simplify the inequality
To isolate the term involving $s$, subtract $10$ from both sides: $$ 8.95s < 115 - 10 $$ $$ 8.95s < 105 $$
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Final form of the inequality
The inequality we derived is: $$ 8.95s < 105 $$ This is the appropriate form to determine the maximum number of shin guards the coach can order.
The inequality that represents the maximum number of shin guards the coach can order is: $$ 8.95s + 10 < 115 $$
More Information
This inequality shows that the total cost of purchasing $s$ pairs of shin guards, plus the shipping fee, must be under $115. Solving for $s$ will provide the maximum number of shin guards the coach can afford.
Tips
- A common mistake is forgetting to include the shipping cost in the total. Always remember to account for all costs involved.
- Another mistake is flipping the inequality symbol incorrectly when manipulating the equation. Be careful when subtracting or dividing.
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