Part 1: Camron, Ty, and Jack are buying some basketball gear for the upcoming season. They each need to buy 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.

Answer 1

To set up this problem as an algebraic expression, we first need to determine the total cost of the basketball gear for each person (Camron, Ty, and Jack).

1. Identify the costs:

   • Cost of socks: $5 per pair
   • Cost of shorts: $26 per pair
   • Cost of jerseys: $42 per jersey

2. Determine the quantities needed:

   • Each person needs:
     • 4 pairs of socks
     • 2 pairs of shorts
     • 3 jerseys

3. Calculate the total cost for each item:

   • Total cost for socks for one person: \[ \text{Total socks cost} = 4 \text{ pairs} \times $5/\text{pair} = 20 \]
   • Total cost for shorts for one person: \[ \text{Total shorts cost} = 2 \text{ pairs} \times $26/\text{pair} = 52 \]
   • Total cost for jerseys for one person: \[ \text{Total jerseys cost} = 3 \text{ jerseys} \times $42/\text{jersey} = 126 \]

4. Combine the costs for one person: \[ \text{Total cost for one person} = \text{Total socks cost} + \text{Total shorts cost} + \text{Total jerseys cost} \] Substituting in the values: \[ \text{Total cost for one person} = 20 + 52 + 126 = 198 \]

5. Calculate the total cost for all three people: \[ \text{Total cost for three people} = 3 \times \text{Total cost for one person} = 3 \times 198 = 594 \]

Thus, the algebraic expression for the total cost can be expressed as: \[ \text{Total cost} = 3 \times (4 \times 5 + 2 \times 26 + 3 \times 42) \]

This expression represents the total cost for Camron, Ty, and Jack to purchase their basketball gear.

Answer 2

could you make that less complex?

Answer 3

Certainly! Let’s simplify the explanation and focus on setting up the basic algebraic expression without all the detailed steps.

Given:

• Socks: 4 pairs needed, cost $5 each
• Shorts: 2 pairs needed, cost $26 each
• Jerseys: 3 needed, cost $42 each

Total cost for one person can be expressed as:

\[ \text{Total Cost} = (\text{cost of socks}) + (\text{cost of shorts}) + (\text{cost of jerseys}) \]

Breakdown:

1. Cost for socks: \( 4 \times 5 = 20 \)
2. Cost for shorts: \( 2 \times 26 = 52 \)
3. Cost for jerseys: \( 3 \times 42 = 126 \)

Combine the costs:

\[ \text{Total Cost for one person} = 20 + 52 + 126 \]

For all three people:

\[ \text{Total Cost for three people} = 3 \times (4 \times 5 + 2 \times 26 + 3 \times 42) \]

Final algebraic expression:

You can also express this final cost for three people in a simplified expression: \[ \text{Total Cost} = 3 \times (4 \times 5 + 2 \times 26 + 3 \times 42) \]

This keeps it straightforward and uses a single expression to represent the total cost of all gear.

Answer 4

Show how to set up this problem as an algebraic expression.

Answer 5

To set up the problem as an algebraic expression, we'll focus on the total cost incurred by Camron, Ty, and Jack for their basketball gear. Each person needs the same quantity of items.

Given:

• Each needs:
  • 4 pairs of socks at $5 per pair
  • 2 pairs of shorts at $26 per pair
  • 3 jerseys at $42 each

Setup:

1. Define the costs for one person:

   • Cost of socks for one person: \( 4 \times 5 \)
   • Cost of shorts for one person: \( 2 \times 26 \)
   • Cost of jerseys for one person: \( 3 \times 42 \)

2. Combine these costs into an expression for one person: \[ \text{Total Cost for one person} = (4 \times 5) + (2 \times 26) + (3 \times 42) \]

3. Now, since there are three people, multiply the total for one person by 3: \[ \text{Total Cost for three people} = 3 \times \left[ (4 \times 5) + (2 \times 26) + (3 \times 42) \right] \]

Final Algebraic Expression:

The final algebraic expression representing the total cost for all three players combined is: \[ \text{Total Cost} = 3 \times \left[ (4 \times 5) + (2 \times 26) + (3 \times 42) \right] \]

This expression captures the full cost of the basketball gear for Camron, Ty, and Jack.