Part 1: Setting Up the Algebraic Expression
Each of the three boys (Camron, Ty, and Jack) needs the following gear:
- 4 pairs of socks
- 2 pairs of shorts
- 3 jerseys
We can represent the number of items needed using the following variables:
- \( k \) for socks
- \( s \) for shorts
- \( j \) for jerseys
Since each boy needs the same amount of each item, we can set up expressions for the total number of items needed by all three boys as follows:
\[ \text{Total socks} = 3 \times k = 3 \times 4 = 12 \] \[ \text{Total shorts} = 3 \times s = 3 \times 2 = 6 \] \[ \text{Total jerseys} = 3 \times j = 3 \times 3 = 9 \]
The full algebraic expression representing the total amount of each type of gear for all three boys is:
\[ \text{Total gear} = 3k + 3s + 3j \]
Part 2: Evaluating Total Cost
Now we calculate the total cost of the basketball gear using the given prices:
- Cost of socks = $5 per pair
- Cost of shorts = $26 each
- Cost of jerseys = $42 each
Now calculate the total cost for each item:
-
Total cost for socks: \[ \text{Total cost for socks} = \text{number of socks} \times \text{cost per pair} = 12 \times 5 = 60 \]
-
Total cost for shorts: \[ \text{Total cost for shorts} = \text{number of shorts} \times \text{cost per short} = 6 \times 26 = 156 \]
-
Total cost for jerseys: \[ \text{Total cost for jerseys} = \text{number of jerseys} \times \text{cost per jersey} = 9 \times 42 = 378 \]
Now, we add all the costs together to find the total cost for Camron's, Ty's, and Jack's basketball gear:
\[ \text{Total cost} = \text{Total cost for socks} + \text{Total cost for shorts} + \text{Total cost for jerseys} \] \[ \text{Total cost} = 60 + 156 + 378 \]
Calculating that:
\[ \text{Total cost} = 60 + 156 = 216 \] \[ \text{Total cost} = 216 + 378 = 594 \]
Thus, the total cost for Camron's, Ty's, and Jack's basketball gear altogether is $594.