Part 1: Setting Up the Problem
To set up the algebraic expression for each person's basketball gear costs, we will first define the costs for each item needed.
- Socks: $5 per pair
- Shorts: $26 each
- Jerseys: $42 each
Let's denote:
- \( S \): number of pairs of socks (4 pairs)
- \( H \): number of pairs of shorts (2 pairs)
- \( J \): number of jerseys (3 jerseys)
Now, we can express the total cost (C) for one person as follows: \[ C = (5S) + (26H) + (42J) \] Substituting in the values for \( S \), \( H \), and \( J \): \[ C = (5 \times 4) + (26 \times 2) + (42 \times 3) \]
Part 2: Solving for Total Cost
Now, we compute the total cost for one person first and then multiply that by the number of people (3: Camron, Ty, and Jack).
First, calculate the individual total cost: \[ C = (5 \times 4) + (26 \times 2) + (42 \times 3) \]
Calculating each term:
- Socks: \( 5 \times 4 = 20 \)
- Shorts: \( 26 \times 2 = 52 \)
- Jerseys: \( 42 \times 3 = 126 \)
Now, add these costs together: \[ C = 20 + 52 + 126 = 198 \]
This is the cost for one person. To find the total cost for Camron, Ty, and Jack, we multiply by 3: \[ \text{Total Cost} = 3 \times 198 = 594 \]
Part 3: Explanation of the Solution
To solve for the total cost of Camron's, Ty's, and Jack's basketball gear:
- We set up the algebraic expression based on the costs of items they each need.
- We calculated the total cost for one individual by substituting the number of items they needed into the cost equation, leading us to a total of $198 for one person.
- Finally, since there are three individuals buying the same amount of gear, we multiplied the individual total cost ($198) by 3 to arrive at the final total cost of $594 for all three players combined.
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