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Applications
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Steps for solving word problems:
1. Identify the variable (What is the quantity are we
trying to find).
2. Express all unknown quantities in terms of one
variable.
3. Set-up the equation.
4. Solve the equation and check your answer.
Example:
Find the consecutive integers whose sum is 147.
1st step- Identify the variable
x = first integer
2nd step- Express all unknown quantities in terms of the
one variable.
x + 1 = second integer
x +2 = third integer
3rd step- Set-up the equation
x + (x + 1) + (x + 2 ) = 147
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4th step- Solve
x + (x + 1) + (x + 2 ) = 147
3x + 3 = 147
3x = 144
3x 144
=
3
3
x = 48
x + 1 = 49
x + 2 = 50
Check: 48 + 49+ 50 = 147
147 = 147
Example 1:
Find three consecutive even integers whose sum is 222.
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Example 2:
The length of a rectangular garden is 20 feet more than
the width. The perimeter is 140 feet. What are the
dimensions of the garden?
Example 3:
Heather has $2.40 in quarters and nickels. She has a
total of 24 coins. How many nickels does she have?
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Example 4:
A coin purse contains an equal number of nickels,
dimes and quarters. If the total amount in the coin
purse is $1.60. How many of each coin is in the coin
purse?
Example 5:
The length of the rectangle is 7 feet more than twice
the width. The area of the rectangle is
30 sq. ft. What are the dimensions of the rectangle?
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Example 6:
Area of a triangle is 18 sq. ft. The base is 5 ft. more
than the height. Find the length of the base and the
height of the triangle?