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2-9A Solving Equations
from Word Problems
Basic Amount/Sum Problems
Rectangle Problems
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
There are 54
54 kilograms of apples in two baskets. The second basket
of apples weighs 12 kilograms more than the first. How many
kilograms are in each basket?
Assign Labels.
let f = first
basket
f
let (f
12
12)= second basket
f ++12
Verbal Model
first basket + second basket = total
Algebraic Model.
(Equation)
Solve.
+
=
f  f  12  54
2f  12  54
 12  12
2f  42
2
2
f  21
(21)  12
33
Why is it f+12
Sentence.
and not 12+f?
Remove parentheses
when there is an
addition sign beside it.
There are 21 kg of apples in the first
basket and 33 kg in the second basket.
Does 21 and 33 equal 54?
Does the second basket weigh 12 kg
more than the first basket?
The length of a rectangle is 8cm longer than twice the width. If the
perimeter is 34 find the dimensions of the rectangle.
length
Labels.
Let w = width
Let(2w
2w
8 = length
8)
2
w + 8
width
width
length
lengths
V.M.
+ twoof
widths
Perimeter
= two
Remember when
asked for
the
dimensions
a rectangle, you are

 and the length.
being asked for the measurement
 of the
 width
+ 2
A.M.
= 2
Solve.
Sentence.
Check
34  4w  16  2w
34  6w  16
 16
 16
18  6w
6 6
3w
23  8
68
14
The width is 3cm and the length is 14cm.
Perimeter = 2 lengths + 2 widths
34 = 2(14) + 2(3)
34 = 28 + 6

34 = 34
Is the length twice
the width plus 8?
The length of a rectangle is 8cm longer than twice the width. If the
perimeter is 34 find the dimensions of the rectangle.
length
Labels.
Let w = width
Let 2w + 8 = length
V.M.
Perimeter = two lengths + two widths
A.M.
34 = 2 (2w + 8) + 2 w
width
width
length
Complete the steps highlighted above for the seven class work
problems. When you have finished those steps, go back and
solve the equations.
Example 1 The sum of the ages of two sisters is 25.
25 The second
sister’s age is 5 more than three times the first sister’s age. Find
the two ages.
Assign Labels.
Verbal Model.
Algebraic Model.
Solve.
Sentence.
Let f = first sister’s age
Let 3
3f
f + 55 = second sister’s age
first sister’s age + second sister’s age =total
+
=
f  3f  5  25
4f  5  25
5 5
35  5
4f  20
4 4
15  5
f5
20
The first sister is 5 and the second sister is 20.
Example 2 A carpenter cut a board that was 10 feet long into two
pieces. The longer piece is two feet longer than three times the
length of the shorter piece. What is the length of each piece?
Assign Labels.
Verbal Model.
Algebraic Model.
Solve.
Sentence.
Let s = short board
3ss
Let 3
3s
+22 = long board
short board + long board = total
+
=
s  3s  2  10
4s  2  10
2 2
4s  8
4 4
s 2
The short board is 2 feet and
the long board is 8 feet long.
32  2
62
8
Example 3 The length of a rectangle is 1 meter less than twice its
width. If the perimeter is 112 meters, find the dimensions.
Labels.
V.M.
A.M.
Solve.
Sentence.
Let w = width
Let(2w
2w
1 = length
2
w - 11)
Perimeter = two lengths + two widths


  
+
2
112 = 2
length
width
width
length
112  4w  2  2w
112  6w  2
219  1
2
2
38  1
114  6w
37
6
6
19  w
The width is 19 meters and the length is 37 meters.
Example 4 The length of a rectangle is twice its width. If the
perimeter is 60 meters, find the dimensions (length and width) of the
rectangle.
Labels.
V.M.
A.M.
Solve.
Sentence.
Let w = width
Let(2w)
2w
2w= length
Perimeter = two lengths + two widths


  
+
2
60 = 2
60  4w  2w
60  6w
6
6
10  w
length
width
width
length
210 
20
The width is 10 meters and the length is 20 meters.
Example 5 There are three numbers. The first is twice as big as
the second, and the second is twice as big as the third. The total
of the numbers is 224. What are the numbers?
Assign Labels.
Verbal Model.
Algebraic Model.
Solve.
Sentence.
Check
Let t = third number
Let 2t = second number
Let 2(2t) = first number
first # + second # + # number = total
22t   2t  t  224
4t  2t  t  224
7t  224
7
7
t  32
2232
232 264 
64
128
The number are 32, 64, and 128.
32  64  128  224
Example 6 Mary and Betty have saved $43. Betty has saved $3
more than three times the amount Mary has saved. How much
money has each girl saved?
Assign Labels.
Verbal Model.
Algebraic Model.
Solve.
Sentence.
Let m = Mary’s savings
Let 3m + 3 = Betty’s savings
Mary’s savings + Betty’s savings = total
m  3m  3  43
4m  3  43
3 3
310   3
4m  40
4
30  3
4
33
m  10
Mary saved $10 and Betty saved $33.
Example 7 Marge worked three times as many problems as Sue. They
worked a total of 32 problems. How many problems did Sue work?
Assign Labels.
Let s = Sue’s problems
Verbal Model.
Let 3s = Marge’s problems
Sue’s problems + Marge’s problems = total
Algebraic Model.
Solve.
Sentence.
Check
s  3s  32
4s  32
4 4
s8
Sue worked 8 problems.
38
24
24  8  32
2-A13 Handout A13