1. Equations and Problem Solving
Mrs. Book

2. Value in cents of q quarters Twice the length l
Bellwork
Value in cents of q quarters
Twice the length l
Cost of n items at $3.99 per item

3. Defining One Variable in Terms of Another
The length of a rectangle is 6 in. more than its width. The perimeter of the rectangle is 24 in. What is the length of the rectangle?
Let w = the width
Then w + 6 = the length
P = 2l + 2w
24 = 2(w + 6) + 2(w)

4. Defining One Variable in Terms of Another
24 = 2(w + 6) + 2(w) Distribute
24 = 2w w Combine Like Terms
24 = 4w + 12
Subtraction Property of Equality
12 = 4w
Division Property of Equality
3 = w Simplify

5. Consecutive Integer Problem
The sum of three consecutive integers is Find the integers
Let n = the first integer
Let n + 1 = the second integer
Let n + 2 = the third integer
n + (n + 1) + (n + 2) = 147

6. Consecutive Integer Problem
n + (n + 1) + (n + 2) = 147
Distribute
n + n n + 2 = 147
Combine Like Terms
3n + 3 = 147 Subtract
3n = 144 Divide
n = 48 Simplify

7. Same-Direction Travel
A train leaves a train station at 1 pm. It travels at an average rate of 72 mi/h. A high- speed train leaves the same station an hour later. It travels at an average rate of 90 mi/h. The second train follows the same route as the first train on a track parallel to the first. In how many hours will the second train catch up with the first train?

8. Same-Direction Travel
Let t = the time the first train travels
Then t – 1 = the time the second train travels
Train 1 travels at 72 mi/h, so 72t represents the distance traveled
Train 2 travels at 90 mi/h, so 90(t – 1) represents the distance traveled

9. Same-Direction Travel
We want to determine when they will be at the same place
72t = 90 (t – 1)

10. Same-Direction Travel
72t = 90t – 90 Distribute
-18t = -90
Move the variable to one side
t = 5 Division Property of Equality
The second train travels t - 1 hours so it only takes 4 hours for the second train to catch up with the first train.

11. Round-Trip Travel
Noya drives into the city to buy a software program at a computer store. Because of traffic conditions, she averages only 15 mi/h. On her drive home, she averages 35 mi/h. If the total travel time is 2 hours, how long does it take her to drive to the computer store.

12. Round-Trip Travel Let t = time of Noya’s drive to the computer store
2 – t = the time of Noya’s drive home
She averages 15 mi/h to the computer store, so 15t represents the distance
She averages 35 mi/h on the drive home, so 35(2 – t)

13. Round-Trip Travel 15t = 35( 2 – t ) 15t = 70 – 35t Distribute
Move the variable to one side
50t = 70 Combine like terms
t = 1 ⅖ Division Property of Equality

14. Opposite-Direction Travel
Jane and Peter leave their home traveling in opposite directions on a straight road. Peter drives 15 mi/h faster than Jane. After 3 hours they are 225 miles apart. Find Peter’s rate and Jane’s rate.

15. Opposite-Direction Travel
Let r = Jane’s rate
Then r + 15 = Peter’s rate
Jane’s distance is 3r
Peter’s distance is 3(r + 15)
3r + 3(r + 15) = 225

16. Opposite-Direction Travel
3r + 3(r + 15) = 225
3r + 3r + 45 = 225 Distribute
6r + 45 = 225 Combine Like Terms
6r + 45 – 45 = 225 – 45 Subtraction
6r = 180 Simplify
r = 30 Division Property of Equality