Question

3 boys are buying basketball gear. They each need 4 pairs of socks, 2 pairs of shorts, and 3 jerseys. The socks cost $5 a pair, the shorts cost $26 each, and the jerseys cost $42 each. Show how to set up this problem as an algebraic expression. Then solve

Answer 1

Let's define the variables and set up the problem step by step.

1. **Identify the costs of each item:**
- Cost of socks per pair = $5
- Cost of shorts per pair = $26
- Cost of jerseys per item = $42

2. **Determine the quantity needed:**
Each boy needs:
- 4 pairs of socks
- 2 pairs of shorts
- 3 jerseys

3. **Calculate the total cost for one boy:**
To find the total cost per boy, we can set up the following expression:

\[
\text{Total Cost for one boy} = (\text{Cost of socks} \times \text{Number of socks}) + (\text{Cost of shorts} \times \text{Number of shorts}) + (\text{Cost of jerseys} \times \text{Number of jerseys})
\]

Plugging in the values for one boy:

\[
\text{Total Cost for one boy} = (5 \text{ dollars/pair} \times 4 \text{ pairs}) + (26 \text{ dollars/pair} \times 2 \text{ pairs}) + (42 \text{ dollars/jersey} \times 3 \text{ jerseys})
\]

Let's simplify each term:

- Cost of socks: \( 5 \times 4 = 20 \) dollars
- Cost of shorts: \( 26 \times 2 = 52 \) dollars
- Cost of jerseys: \( 42 \times 3 = 126 \) dollars

Now, add these amounts together to get the total cost for one boy:

\[
\text{Total Cost for one boy} = 20 + 52 + 126
\]
\[
\text{Total Cost for one boy} = 198 \text{ dollars}
\]

4. **Calculate the total cost for 3 boys:**
Since there are 3 boys, we multiply the total cost for one boy by 3:

\[
\text{Total Cost for 3 boys} = 198 \times 3
\]
\[
\text{Total Cost for 3 boys} = 594 \text{ dollars}
\]

Thus, the total cost for the basketball gear for all 3 boys is **$594**.