1. Solving Equations from Word Problems
Basic Amount/Sum Problems
Rectangle Problems
Algebra Krista Craig

2. when there is an addition sign beside it.
There are 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? 54
Assign Labels.
let f = first basket f
let f + 12 = second basket
(f + 12)
Verbal Model
first basket + second basket = total + =
Algebraic Model.
(Equation)
Solve.
Why is it f+12 and not 12+f?
Sentence.
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?

3. The width is 3cm and the length is 14cm. Sentence.
The length of a rectangle is 8cm longer than twice the width. If the perimeter is 34 find the dimensions of the rectangle. 34
length
Labels.
Let w = width w
Let 2w + 8 = length
(2w + 8)
width
width
length
V.M.
Remember when asked for the dimensions of a rectangle, you are being asked for the measurement of the width and the length.
Perimeter =
two lengths +
two widths     
A.M. = 2 + 2
Solve.
The width is 3cm and the length is 14cm.
Sentence.
Check
Perimeter = 2 lengths + 2 widths
Is the length twice the width plus 8?
34 = 2(14) + 2(3)
34 = 
34 = 34

4. The length of a rectangle is 8cm longer than twice the width
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
width
width
length
V.M.
Perimeter =
two lengths +
two widths
A.M. 34 = 2
(2w + 8) + 2 w
Complete the steps highlighted above for the seven class work problems. When you have finished those steps, go back and solve the equations.

5. Example 1 The sum of the ages of two sisters is 25
Example 1 The sum of the ages of two sisters is 25. The second sister’s age is 5 more than three times the first sister’s age. Find the two ages.
Assign Labels.
Let f = first sister’s age
Let 3f + 5 = second sister’s age
Verbal Model.
first sister’s age + second sister’s age =total + =
Algebraic Model.
Solve.
The first sister is 5 and the second sister is 20.
Sentence.

6. short board + long board = total
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.
Let s = short board
Let 3s + 2 = long board
Verbal Model.
short board + long board = total + =
Algebraic Model.
Solve.
The short board is 2 feet and the long board is 8 feet long.
Sentence.

7. The width is 19 meters and the length is 37 meters.
Example 3 The length of a rectangle is 1 meter less than twice its width. If the perimeter is 112 meters, find the dimensions.
length
Labels.
Let w = width w
Let 2w - 1 = length
(2w - 1)
width
width
V.M.
Perimeter =
two lengths +
two widths
length     
A.M.
112 = 2 + 2
Solve.
Sentence.
The width is 19 meters and the length is 37 meters.

8. The width is 10 meters and the length is 20 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.
length
Labels.
Let w = width w
Let 2w = length
(2w)
width
width
V.M.
Perimeter =
two lengths +
two widths
length     
A.M. 60 = 2 + 2
Solve.
Sentence.
The width is 10 meters and the length is 20 meters.

9. Example 5 There are three numbers
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 What are the numbers?
Assign Labels.
Let t = third number
Let 2t = second number
Let 2(2t) = first number
Verbal Model.
first # + second # + # number = total
Algebraic Model.
Solve.
The number are 32, 64, and 128.
Sentence.
Check

10. Example 6 Mary and Betty have saved $43
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.
Let m = Mary’s savings
Let 3m + 3 = Betty’s savings
Verbal Model.
Mary’s savings + Betty’s savings = total
Algebraic Model.
Solve.
Mary saved $10 and Betty saved $33.
Sentence.

11. Example 7 Marge worked three times as many problems as Sue
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
Let 3s = Marge’s problems
Verbal Model.
Sue’s problems + Marge’s problems = total
Algebraic Model.
Solve.
Sue worked 8 problems.
Sentence.
Check