Part 1: Setting Up the Algebraic Expression
To set up the problem as an algebraic expression, we need to calculate the total cost for each person (Camron, Ty, and Jack) based on their requirements for socks, shorts, and jerseys.
Let:
- \( S \) = cost of socks
- \( H \) = cost of shorts
- \( J \) = cost of jerseys
Given:
- Cost of socks = $5 per pair
- Cost of shorts = $26 each
- Cost of jerseys = $42 each
Each person needs:
- 4 pairs of socks
- 2 pairs of shorts
- 3 jerseys
The expression for the total cost for one person can be set up as follows:
\[ \text{Total Cost for one person} = (4 \times 5) + (2 \times 26) + (3 \times 42) \]
The total cost for all three people (Camron, Ty, and Jack) will be:
\[ \text{Total Cost for three people} = 3 \times \left( (4 \times 5) + (2 \times 26) + (3 \times 42) \right) \]
Part 2: Solving the Total Cost
Now we can calculate the total cost for one person first:
-
Calculate the cost of socks: \[ 4 \times 5 = 20 \]
-
Calculate the cost of shorts: \[ 2 \times 26 = 52 \]
-
Calculate the cost of jerseys: \[ 3 \times 42 = 126 \]
Now, sum these costs for one person: \[ \text{Total Cost for one person} = 20 + 52 + 126 = 198 \]
Now, to find the total cost for all three people: \[ \text{Total Cost for three people} = 3 \times 198 = 594 \]
Part 3: Explanation of the Solution
In Part 2, I began by calculating the total expenses for one person by individually determining the cost of each item they needed: socks, shorts, and jerseys. I multiplied the quantity of each item by its respective cost, and then summed all these values.
After calculating the total cost for one person, I multiplied that result by 3 (since there are three people: Camron, Ty, and Jack) to get the overall total cost for everyone’s basketball gear.
The final result obtained from these calculations is $594, which is the total amount they will need to spend on basketball gear together.
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