Question

1. two companies offer elizabeth a sales position. company a pays $3,500 per month plus $275 per car sold. company b pays $3,000 per month plus $350 per car sold. which equation could be used to determine the number of cars sold in a month, x, that would result in the same total income from each company?

a) $3,500 - 275x = 3,000 + 350x$
b) $3,500 + 275x = 3,000 + 350x$
c) $3,500x - 275 = 3,000x - 350$
d) $3,500x + 275 = 3,000x + 350$
6a) solve $0.1(x + 8) - 0.5x = 0.2(2x - 6) + 5.2$.
6b) which equation illustrates the distributive property?
a) $0.4(2x - 2) + 8.4 = 0.8x - 0.8 + 8.4$
b) $0.1x + 0.6 - 0.7x = -0.6x + 0.6$
c) $0.8x + 0.6x + 7.6 = 1.4x + 7.6$
d) $\frac{1.4x}{1.4} = x$

1. the equation $\frac{4}{5}d - 5 = \frac{3}{5}d - 2$ represents the number of dimes, d, in a stack. how many dimes are in the stack?

Explanation:

Question 5

Step1: Analyze Company A's income

Company A pays a fixed $3500 per month plus $275 per car sold. So if \( x \) cars are sold, the income is \( 3500 + 275x \).

Step2: Analyze Company B's income

Company B pays a fixed $3000 per month plus $350 per car sold. So if \( x \) cars are sold, the income is \( 3000 + 350x \).

Step3: Set incomes equal

To find when the incomes are the same, set the two expressions equal: \( 3500 + 275x = 3000 + 350x \).

Step1: Distribute terms

Distribute \( 0.1 \) and \( 0.2 \): \( 0.1x + 0.8 - 0.5x = 0.4x - 1.2 + 5.2 \).

Step2: Combine like terms

Left side: \( 0.1x - 0.5x + 0.8 = -0.4x + 0.8 \). Right side: \( 0.4x + 4 \).

Step3: Move variables to left

Add \( 0.4x \) to both sides: \( -0.4x + 0.4x + 0.8 = 0.4x + 0.4x + 4 \) → \( 0.8 = 0.8x + 4 \).

Step4: Move constants to right

Subtract 4: \( 0.8 - 4 = 0.8x \) → \( -3.2 = 0.8x \).

Step5: Solve for \( x \)

Divide by \( 0.8 \): \( x = \frac{-3.2}{0.8} = -4 \).

The distributive property is \( a(b + c) = ab + ac \). Option A uses \( 0.4(2x - 2) = 0.8x - 0.8 \), which is distributing \( 0.4 \) over \( 2x - 2 \). Other options: B is combining like terms, C is combining like terms, D is division.

Answer:

B) \( 3,500 + 275x = 3,000 + 350x \)

Question 6A