1.)Mr. Williams weighs 300 pounds. He went on the Subway diet and was guaranteed to lose 5 pounds per week. Write an equation that could be used to find how many weeks, w, it would take for him to weigh 150 pounds.

How many weeks would it take?

2.)The total bill for repairing Troy’s car was $527.63. He paid $210 for parts and the rest of the bill was labor. The technicians that fixed his car charge $52 per hour. Write an equation that could be used to find, t, the length of time it took to fix the car.

How long did it take to get the car fixed?

3.)You have $60 and your sister has $120. You are saving $7 per week and she is saving $5 per week. How long will it take before you and your sister have the same amount of money? Write an equation and solve.(HINT: THIS PROBLEM SHOULD HAVE THE SAME VARIABLE ON BOTH SIDES)

what is the equation and solution ?

4.)SAT Prep If the length of a rectangular parking lot is 3 times its width and its perimeter is 840 yards, what is the length of the parking lot, in yards?

1)Since he can lose 5 pounds per week, this is a linear rate. The weight is decreasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1)d

n = number of terms(weeks)

d = common difference(5 pounds)

a= first term(300 pounds)

The equation that could be used to find how many weeks, w, it would take for him to weigh 150 pounds would be

150 = 300 + (w - 1)5

150 - 300 = 5w - 5

- 150 + 5 = 5w

w = 145/5 = 29 weeks

2) t represents the number of hours used to fix the car. The cost of t hours is 52t. Total amount paid is 210 + 52t. The equation that could be used to find, t, the length of time it took to fix the car is

210 + 52t = 527.23

3) 52t = 527.23 - 210 = 317.23

t = 317.23/52

t = 6 hours

3) Let x represent the time it will take before you and your sister have the same amount of money. The amount that you would have in x weeks is 60 + 7x

The amount that you sister will have in x weeks is 120 + 5x. The equation would be

60 + 7x = 120 + 5x

7x - 5x = 120 - 60

2x = 60

x = 60/2 = 30 weeks

4) let L represent the length of the parking lot.

let W represent the width of the parking lot.

If the length of a rectangular parking lot is 3 times its width, it means that

L = 3W

Its perimeter is 840 yards. It means that

2(L + W) = 840

L + W = 840/2 = 420

Substituting, it becomes

3W + W = 420

4W = 420

W = 420/4 = 105

L = 3 × 105 = 315

Length = 315 yards