Question

Math Quick Check. 1 Correct Answer Per Question.

1. Evaluate the expression for a=4, b=2, and c=8. (You will get a single number for your answer.)
Solve
3a−2b +5c=?

2. Evaluate the expression for x=1.2 and y=5.
3x + 5.7y
a. 32.1
b. 14.9
c. 21.84
d. 3.6

3. -4(3x - 7)
a. 12x + 24
b. -12x - 28
c. -12x + 28
d. -1x - 11

4. 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.

Part 2: Solve to find out how much Camron's, Ty's, and Jack's basketball gear will cost all-together.

Part 3: Explain how you solved for your answer in Part 2.

Answer 1

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:**
1. 48
2. a. 32.1
3. c. -12x + 28
4. Total Cost: 594, with breakdown as explained.