Question

Write an algebraic expression for 3 boys each needing 4 pair of socks, 2 pair of shorts, and 3 jerseys. Socks cost $5 each , shorts $26each, and the jerseys cost $42 each

Answer 1

To write an algebraic expression for the total cost of the clothing items needed by the 3 boys, we can break it down step by step.

1. **Calculate the total number of each item needed**:
- **Socks**: Each boy needs 4 pairs of socks. For 3 boys, the total is:
\[
3 \text{ boys} \times 4 \text{ pairs of socks/boy} = 12 \text{ pairs of socks}
\]

- **Shorts**: Each boy needs 2 pairs of shorts. For 3 boys, the total is:
\[
3 \text{ boys} \times 2 \text{ pairs of shorts/boy} = 6 \text{ pairs of shorts}
\]

- **Jerseys**: Each boy needs 3 jerseys. For 3 boys, the total is:
\[
3 \text{ boys} \times 3 \text{ jerseys/boy} = 9 \text{ jerseys}
\]

2. **Calculate the cost of each item**:
- The cost of socks is $5 per pair:
\[
\text{Cost of socks} = 12 \text{ pairs} \times 5 = 60
\]

- The cost of shorts is $26 per pair:
\[
\text{Cost of shorts} = 6 \text{ pairs} \times 26 = 156
\]

- The cost of jerseys is $42 each:
\[
\text{Cost of jerseys} = 9 \text{ jerseys} \times 42 = 378
\]

3. **Combine the costs into an algebraic expression**:
Now, we can write the total cost \( C \) as the sum of the costs of all items:
\[
C = (12 \times 5) + (6 \times 26) + (9 \times 42)
\]

4. **Substituting in the calculations**:
\[
C = 60 + 156 + 378
\]

5. **Final algebraic expression**:
Thus, the algebraic expression for the total cost of the clothing items needed by the 3 boys is:
\[
C = 12 \times 5 + 6 \times 26 + 9 \times 42
\]

To find the total cost, you can also calculate that:
\[
C = 60 + 156 + 378 = 594
\]

So, the total cost \( C \) is $594.