Let’s solve each of the questions step-by-step.
1. Evaluate the expression for a=4, b=2, and c=8.
Expression: \( 3a - 2b + 5c \)
Substituting the values: \( 3(4) - 2(2) + 5(8) \)
Calculating:
- \( 3(4) = 12 \)
- \( -2(2) = -4 \)
- \( 5(8) = 40 \)
Now combine them: \( 12 - 4 + 40 = 48 \)
Answer: 48
2. Evaluate the expression for x=1.2 and y=5.
Expression: \( 3x + 5.7y \)
Substituting the values: \( 3(1.2) + 5.7(5) \)
Calculating:
- \( 3(1.2) = 3.6 \)
- \( 5.7(5) = 28.5 \)
Now combine them: \( 3.6 + 28.5 = 32.1 \)
The correct option is: a. 32.1
3. Simplify the expression: -4(3x - 7)
Distributing -4: \( -4(3x) + -4(-7) \)
Calculating:
- \( -4(3x) = -12x \)
- \( -4(-7) = 28 \)
Combined expression: c. -12x + 28
4. Part 1: Set up the algebraic expression for the costs.
Let:
- Socks cost = $5 each
- Shorts cost = $26 each
- Jerseys cost = $42 each
For each person:
- Cost for socks: \( 4 \times 5 \)
- Cost for shorts: \( 2 \times 26 \)
- Cost for jerseys: \( 3 \times 42 \)
Total cost for one person: \( (4 \times 5) + (2 \times 26) + (3 \times 42) \)
For all three: \( 3 \times ((4 \times 5) + (2 \times 26) + (3 \times 42)) \)
Part 2: Solve to find the total cost.
Individual cost:
- Socks: \( 4 \times 5 = 20 \)
- Shorts: \( 2 \times 26 = 52 \)
- Jerseys: \( 3 \times 42 = 126 \)
Total cost for one person: \( 20 + 52 + 126 = 198 \)
Total for all three: \( 3 \times 198 = 594 \)
Total Cost: 594
Part 3: Explanation of how I solved for the total cost.
I set up the individual costs for socks, shorts, and jerseys using multiplication for quantities and prices. I then added these costs together to get the total for one person, and finally multiplied that amount by 3 to account for all three individuals buying the same gear.
Final Answers:
- 48
- a. 32.1
- c. -12x + 28
- Total Cost: 594, with breakdown as explained.