Part 1: Setting Up the Algebraic Expression
Let's denote:
- \( S = 5 \) (cost of one pair of socks)
- \( H = 26 \) (cost of one pair of shorts)
- \( J = 42 \) (cost of one jersey)
Each person (Camron, Ty, and Jack) needs to buy:
- 4 pairs of socks: \( 4S \)
- 2 pairs of shorts: \( 2H \)
- 3 jerseys: \( 3J \)
The total cost for one person can be expressed as: \[ \text{Total cost for one person} = 4S + 2H + 3J \]
To find the total cost for all three individuals, we multiply this expression by 3: \[ \text{Total cost for three people} = 3(4S + 2H + 3J) \]
Part 2: Solving the Expression
Now we substitute the values of \( S \), \( H \), and \( J \) into the expression: \[ \text{Total cost for one person} = 4(5) + 2(26) + 3(42) \]
Calculating each term:
- \( 4S = 4 \times 5 = 20 \)
- \( 2H = 2 \times 26 = 52 \)
- \( 3J = 3 \times 42 = 126 \)
Now, add these amounts together: \[ \text{Total cost for one person} = 20 + 52 + 126 = 198 \]
Next, this amount is multiplied by 3 to account for Camron, Ty, and Jack: \[ \text{Total cost for three people} = 3 \times 198 = 594 \]
Part 3: Explanation of the Solution
To find the total cost of basketball gear for Camron, Ty, and Jack, I first set up an expression representing the cost for one person based on the number of socks, shorts, and jerseys they need, along with their respective prices. By simplifying the expression (calculating for one person), I found that the total cost for one person was $198.
Finally, since there are three people buying the same gear, I multiplied the individual total cost by 3, resulting in a final amount of $594 for all three individuals. Thus, the total cost of basketball gear for Camron, Ty, and Jack together is $594.
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