A. Solving by Combining Like Terms
5h + 2 + 2h = 23
h = 3
2(x + 5) = 14
x = 2
8b + 3b + 2 = 4b+9
b = 1
4x = 32
x = 8
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.
3b + b - 8 = 4
b = 3
5(d - 2) = 40
d = 10
19x - 24x=20-5
x = -3
x + 3x = -8
x = -2
Mr. Cushman bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Cushman buy?
n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99
3a + 12 - 6a = -9
a = 7
7(4 - t) = -84
t = 16
3 + 5(a + 4) = 4a + 25
a = 2
4(y - 2) = -12
y = -1
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.
-6 = -3y + 4 + 5y
y = -5
-2(x - 9) = -24
x = 21
-1 (2b - 4) = 3b + 2
b = 2/5
-6(m + 1) + 18 = 24
m = -2
Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?
r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87
78 = 3c + 12 - c + 4
c = 31
-13(4 + 2a) = 208
a = -10
7(t + 3) = 5t + 27
t = 3
2(k + 12) + 7k = 51
k = 3
When you count by ones from any 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.