Question

1. a company loses $5,400 as the result of a manufacturing defect. each of the 8 owners have agreed to pay an equal amount, x, to pay for the loss.

part a
write an expression to show the total loss after the owners contribute some money.

part b
how much did each owner contribute if the total loss is $600 after their contributions?

1. a car travels $2\frac{5}{8}$ miles in $3\frac{1}{2}$ minutes at a constant speed. how far did the car travel in 5 minutes?

1. select all the expressions that are equivalent to $9 + 7x - 3y$.

$9 + 7x + 3y$
$9 - 7x - 3y$
$9 - 7x + 3y$
$9 + 7x + (-3y)$
$9 - (-7)x - 3y$

Explanation:

Problem 1 Part A

Step1: Define total loss after payment

Total initial loss minus total owner contributions.
Expression: $5400 - 8x$

Problem 1 Part B

Step1: Set up equation for final loss

Final loss equals initial loss minus total contributions.
$600 = 5400 - 8x$

Step2: Rearrange to solve for $8x$

Subtract 600 and add $8x$ to both sides.
$8x = 5400 - 600$

Step3: Calculate total owner contributions

Compute the difference.
$8x = 4800$

Step4: Solve for $x$

Divide total contributions by number of owners.
$x = \frac{4800}{8} = 600$

Problem 2

Step1: Convert mixed numbers to fractions

Rewrite distance and time as improper fractions.
$2\frac{5}{8} = \frac{21}{8}$ miles, $3\frac{1}{2} = \frac{7}{2}$ minutes

Step2: Calculate speed (miles per minute)

Speed = distance divided by time.
$\text{Speed} = \frac{\frac{21}{8}}{\frac{7}{2}} = \frac{21}{8} \times \frac{2}{7} = \frac{3}{4}$ miles/min

Step3: Find distance in 5 minutes

Distance = speed multiplied by time.
$\text{Distance} = \frac{3}{4} \times 5 = \frac{15}{4} = 3\frac{3}{4}$

Problem 3

Step1: Analyze equivalent expressions

Use sign rules: $a - b = a + (-b)$, $-(-c) = c$.

• $9+7x+(-3y) = 9+7x-3y$
• $9-(-7)x-3y = 9+7x-3y$

Answer:

1. Part A: $5400 - 8x$

Part B: $\$600$

1. $3\frac{3}{4}$ miles

3.

• $\square$ $9 + 7x + 3y$
• $\square$ $9 - 7x - 3y$
• $\square$ $9 - 7x + 3y$
• $\blacksquare$ $9 + 7x + (-3y)$
• $\blacksquare$ $9 - (-7)x - 3y$