2 Algebraic Models
2 Creating and Solving Equations
Creating and Solving Equations
I
can create and solve equations involving
the distributive property.
I
can create and solve equations with
variables on both sides.
Write an equation for each description.

The sum of 14 and a number is equal to 17.
14 + x = 17

The difference between a number and 12 is 20.
x – 12 = 20

Two-thirds of a number plus 4 is 7.

Ten times the sum of half a number and 6 is 8.
2
𝑥+4=7
3
10

1
𝑥+6 =8
2
Hector is visiting a cousin who lives 350 miles away. He has
driven 90 miles. How many more miles does he need to drive to
reach his cousin’s home? 90 + x = 350
Write and solve an equation for each
situation. (#9)

In one baseball season, Peter hit twice the difference of the
number of home runs Alice hit and 6. Altogether, they hit 18
home runs. How many home runs did each player hit that
season?
Peter  2(x - 6)
Alice  x
x + 2(x – 6) = 18
x + 2x – 12 = 18
3x – 12 = 18
+ 12 +12
3x
= 30
3
3
x = 10
Alice hit 10 home runs and Peter hit 8 home runs.
Write and solve an equation for each
situation. (#11)

One month, Ruby worked 6 hours more than Isaac, and Sue
worked 4 times as many hours as Ruby. Together they worked
126 hours. Find the number of hours each person worked.
Ruby  x + 6
(x + 6) + x + 4(x + 6) = 126
Isaac  x
1x + 6 + 1x + 4x + 24 = 126
Sue  4(x + 6)
6x + 30 = 126
- 30 - 30
Ruby = 16 + 6 = 22
6x
= 96
Isaac = 16
6
6
Sue = 4(16 + 6) = 88
x
= 16
Write and solve an equation for each
situation. (#13)

Charles and his cousin Kai both collect stamps. Charles has 56
stamps, and Kai has 80 stamps. The boys recently joined
different stamp-collecting clubs Charles’ club will send him 12
new stamps per month. Kai’s club will send him 8 new stamps
per month. After how many months will Charles and Kai have
the same number of stamps? How many will each have?
Charles  56 + 12m
Kai  80 + 8m
56 + 12m = 80 + 8m
- 8m
- 8m
56 + 4m = 80
-56
-56
4m = 24
4
4
m=6
In 6 months, Charles and Kai will each have 128 stamps.
Write and solve an equation for each
situation. (#15)

Community Gym charges a $50 membership fee and a $55
monthly fee. Workout Gym charges a $200 membership fee and
a $45 monthly fee. After how many months will the total
amount of money paid to both gyms be the same? What will the
amount be?
Community Gym  50 + 55m
Workout Gym  200 + 45m
50 + 55m = 200 + 45m
- 45m
- 45m
50 + 10m = 200
-50
- 50
10m = 150
10
10
m = 15
After 15 months, the amount of money paid to both gyms will be the
same, $875.
Write and solve an equation using the
table to answer each question. (#17)
Company Starting Salary Yearly Salary Increase
A
$24,000
$3000
B
$30,000
$2400
C
$36,000
$2000
After how many years are the salaries offered by Company A and
Company B the same?
24000 + 3000x = 30000 + 2400x
- 2400x
- 2400x
24000 + 600x = 30000
-24000
-24000
600x = 6000
600
600
x = 10
After 10 years, the salaries are the same.
Write and solve an equation using the
table to answer each question. (#19)
Company Starting Salary Yearly Salary Increase
A
$24,000
$3000
B
$30,000
$2400
C
$36,000
$2000
Paul started work at Company B ten years ago at the salary
shown in the table. At the same time, Sharla started at Company
C at the salary shown in the table. Who earned more during the
last year? How much more?
Paul – 30,000 + 2,400(10) = 54,000
Sharla – 36,000 + 2,000(10) = 56,000
Sharla made $2000 more last year.