February 23, 2015
Algebra Word Problems
Consecutive Number Problems
Area Perimeter Problems
Age Problems
February 23, 2015
Find two consecutive integers whose sum is 45.
Set up a legend!
x
22
x+1
23
x + x + 1 = 45
2x + 1 = 45
-1 -1
2x = 44
2x = 44
2
2
Check:
22 + 23 = 45?
x = 22
February 23, 2015
Find three consecutive integers whose sum is 48.
x
x+1
x+2
3x + 3 = 48
-3 -3
3x = 45
3
3
x = 15
February 23, 2015
Find three consecutive even numbers whose sum is 72.
x
x+2
x+4
3x +6 = 72
-6 -6
3x = 66
3 3
x = 22
February 23, 2015
Find four consecutive odd integers whose sum is 56
x
x+2
x+4
x+6
4x + 12 = 56
-12 -12
4x = 44
4x = 44
4
4
x = 11
February 23, 2015
Find three consecutive integers such that the sum of
twice the smallest and three times the largest is 126.
x
2x
x+1
x+2
2x + 3(x +2) = 126
2x + 3x + 6 = 126
3(x + 2)
5x + 6 = 126
-6
-6
5x = 120
x = 24
February 23, 2015
Find two consecutive integers whose sum is -25
x
-12
x -1
-13
2x -1 = -25
+1
+1
2x = -24
x = -12
February 23, 2015
Find three consecutive integers whose sum is -36.
x
-11
x-1
-12
x-2
-13
3x - 3 = -36
+3
+3
3x = -33
x = -11
February 23, 2015
Area / Perimeter Starter
Write an equation for the following diagram and find
the dimensions if the perimeter equals 26
3x - 2
2x
2x
3x - 2
10x - 4 = 26
+4 +4
10x = 30
10x = 30
10 10
x=3
length = 6units
width = 7 units
February 23, 2015
Area / Perimeter Problems
The length of a field is three times its width. If
the perimeter is 96m, find its dimensions.
3x
x
x
3x
Other strategies?
February 23, 2015
Area / Perimeter
The length of a large room is twice its width. If the
perimeter is 72m find its dimensions.
width - x
length - 2x
x + x + 2x + 2x = 72
6x = 72
x = 12
February 23, 2015
Area / Perimeter
If the length of the field is 24m longer than the
width, find its dimensions if the perimeter is 112.
4x + 48 = 112
width - x
4x + 48 = 112
length - x + 24
4x = 64
x = 16
February 23, 2015
Area / Perimeter
The width of a room is one third of its length. If the
perimeter is 144m, find the dimensions.
width - 1 x
3
length - x
other strategies?
1 x + 1 x + x + x = 144
3
3
2 x + 2x = 144
3
3 (2 x + 2x)= 3(144)
3
2x + 6x = 432
8x = 432
x = 54
February 23, 2015
Area / Perimeter
strategy #2
Substitute whole numbers
3x
x
1x
3
x
February 23, 2015
Area / Perimeter
More examples
Substitute whole numbers
2x
x
1x
2
x
February 23, 2015
Area / Perimeter
The width of a garden is two thirds as long as the
length. Find the dimensions if the perimeter is 140.
width - 2 x
3
length - x
Other strategies?
2x + 4 x = 140
3
3( 2x + 4 x)= 3 (140 )
3
6x + 4x = 420
10x = 420
x = 42
February 23, 2015
Area / Perimeter
strategy #2
Substitute whole numbers
3x
x
2x
3
2x
2 is 2 of 3
3
February 23, 2015
Age Problems
Mr Klinker is thirty five and his daughter is ten. In
how many years will Mr. Klinker be twice as old as
his daughter?
Present
Future
Klinker
35
35 + x
2 (10 + x) = 35 + x
Daughter
10
10 + x
20 + 2x = 35 + x
20 + x = 35
x = 15
February 23, 2015
Age Problems
George is seven and his mother is thirty seven. In
how many years will his mother be three times as
old as he is?
3(7 + x) = 37 + x
Present
Future
21 + 3x = 37 + x
George
7
7+x
21 + 2x = 37
Mom
37
37 + x
2x = 16
x=8
February 23, 2015
Age Problems
Dorothy is fourteen years younger than Rita. Ten
years ago, Rita was three times as old as Dorothy
was then. How old is each now?
Past
Present
Dorothy
x - 24
x - 14
Rita
x - 10
x
3(x - 24) = x - 10
3x - 72 = x - 10
2x = 62
x = 31
February 23, 2015
Age Problems
Shirly is two more than four times Rose's age. In
12 years, Rose will be half of Shirley's age. How
old are they today?
Today
Shirley
Rose
Future
4x + 2
4x + 14
x
x+12
x + 12 = 4x + 14
2
2(x + 12) = 4x + 14
2x + 24 = 4x + 14
24 = 2x + 14
10 = 2x
5=x
February 23, 2015
February 23, 2015