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Solving by Combining Like Terms
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Word Problems
100
5h + 2 + 2h = 23
h = 3
100
2(x + 5) = 14
x = 2
100

7n-30=-(-3n+4)-2

n=6

100
4x + 9 = 33
x = 6
100
WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?
n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.
200
3b + b - 8 = 4
b = 3
200
5(d - 2) = 40
d = 10
200

-33+8p=-(-8p+3)+6p

p=-5

200
x + 3x = -8
x = -2
200

Mr. Staub bought 7 One Direction t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many One Direction t-shirts did Mr. Staub buy?

n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99

300
3a + 12 - 6a = -9
a = 7
300
7(4 - t) = -84
t = 16
300

-8x-3(4+8x)=8x-12

x=0

300
4(y - 2) + y = -13
y = -1
300
Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.
400
-6 = -3y + 4 + 5y
y = -5
400
-2(x - 9) = -24
x = 21
400

15-5k=-5(5-3)

All real numbers

400
-6(m + 1) + 18 = 24
m = -2
400

Mr. King goes to the grocery store and purchases 17 rolls of toilet paper and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a roll of toilet paper?

t - cost of a roll of toilet paper 17t + 2.97 = 34.76 t = 1.87 Each roll of toilet paper cost $1.87

500
78 = 3c + 12 - c + 4
c = 31
500
-13(4 + 2a) = 208
a = -10
500

2(8+m)=13+2m

No solution

500

5(1+8x)-4=40-2x+3x

x=1

500

When you count by ones from many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.