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.