Question

1. a service station charges an installation fee of $84 and a set price for each new tire. they charge a total of $791 for four new tires and installation.

part a
let t represent the price of one tire. write an equation that represents the situation.
part b
what is the price, in dollars, of one tire?

1. solve the equation to find the value of x.

$8.35x - 1.5 = 71.98$
a 8.6
b 8.8
c 9
d 10.3

1. the square shown has a perimeter of 35.6 feet. what is the value of x?

$(x + 5.2)$ ft

1. a farmer picks 16 quarts of berries. a recipe for jam requires $2\frac{1}{4}$ quarts of berries to make one batch.

part a
if $2\frac{1}{2}$ quarts of the farmer’s berries cannot be used, which equation represents the number of batches of jam, b, the farmer can make?
a $2\frac{1}{4} = 16 - 2\frac{1}{2}b$
b $16 = 2\frac{1}{2} + 2\frac{1}{4}b$
c $16 = b\left(2\frac{1}{2} + 2\frac{1}{4}\
ight)$
d $2\frac{1}{2} = 16b - 2\frac{1}{4}b$
part b
how many batches of jam can the farmer make?

1. a crate containing 16 bags of powdered milk weighs 63.2 lbs. the weight of the empty crate is 2.4 lbs. select all equations that can be solved to find the weight, b, of one bag of powdered milk.

$63.2 = 18.4b$
$63.2 = 2.4 + 16b$
$60.8 = 16b$
$b = \frac{60.8}{16}$
$60.8b = 16$

Explanation:

Problem 1

Part A

Step1: Identify total cost components

Total cost = installation fee + (price per tire × number of tires)

Step2: Write the equation

Installation fee is $84, number of tires is 4, price per tire is LXI0, total cost is $791. So the equation is \( 84 + 4t = 791 \)

Step1: Start with the equation from Part A

\( 84 + 4t = 791 \)

Step2: Subtract 84 from both sides

\( 4t = 791 - 84 = 707 \)

Step3: Divide both sides by 4

\( t = \frac{707}{4} = 176.75 \)

Step1: Add 1.5 to both sides

\( 8.35x - 1.5 + 1.5 = 71.98 + 1.5 \)
\( 8.35x = 73.48 \)

Step2: Divide both sides by 8.35

\( x = \frac{73.48}{8.35} = 8.8 \)

Answer:

\( 84 + 4t = 791 \)

Part B