Solving by Combining Like Terms
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 (subtract 3 from each side)
n = 8
Julie's sister is 8 years old.
Simplify. 19x - 24x
-5x
Mr. Durst bought 7 Taylor Swift T-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Taylor Swift T-shirts did Mr. Durst buy?
n = number of T-shirts
7n = 90.93 Divide by 7 (on each side of the = sign)
n = 12.99
Each t-shirt cost $12.99
7(4 - t) = -84
t = 16
Simplify. 3 + 5(a + 4)
5a + 23
4(y - 2) + y = -13
y = -1
Super Cool Tyler has 4 boxes of apples. Each box has the same number of apples. After Super Cool 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 (add 3 to each side)
4a = 112 (divide by 4 on each side)
a = 28 There were 28 apples in each box.
Simplify. - (2b - 4)
-2b + 4
-6(m + 1) + 18 = 24
m = -2
Mrs. Higgins goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. Her total cost was $34.76. What was the cost for a bag of raisins?
Why did she buy so many raisins, anyway?
r = cost of a bag of raisins
17r + 2.97 = 34.76 (subtract 2.07 from each side)
17r = 31.79 (divide each side by 17)
r = 1.87
Each bag of raisins cost $1.87
78 = 3c + 12 - c + 4
c = 31
7k - 8 + 2(k + 12) = 52
k = 4
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, and n+2)?
n + n + 1 + n + 2 = 48 (combine like terms)
3n + 3 = 48 (subtract 3 from each side)
3n = 45 (divide each side by 3)
n = 15 (what is n, n+1, and n+2?)
The integers are 15, 16, and 17.