Applied Problems Involving Fractions
We will follow the same method from 181A to solve applied problems that involve fractions.
Example
The width of a piece of paper is 8½ inches. If you want the left and right margins to be 2/3 inches, what is the width of the written part of the page?
Solution
We begin by stating our goal:
"The width of the written part of the page is inches"
Next draw the picture letting x be the width of the written
We see that the total width of 8½ is made up of the two margins and the written space. The margins take up
2 4
2 x
=
3 3
If we take away the margin width from the paper width, we get the width of the writing, that is
1 2
x = 8
-
2 3
17 2
=
-
8 x 2 + 1 = 17
2 3
17 x 3 2 x 2
=
-
The LCD of 2 and 3 is 6
2 x 3 3 x 2
51
4
47
5
=
-
=
= 7
6 x 7 + 5 = 47
6
6
6
6
We can conclude that
The width of the written part of the page is 7 5/6 inches.
Example
You earn 6½ dollars per hour at your job. For over time work you get 1½ times your wages. If you work 4 hour of overtime, how much overtime pay will you get?
Solution
We begin by writing our goal:
"I will earn $ ."
Because of the word "times" we see that this is a multiplication problem. We write
1
1
4
13 3
4 x 6
x 1
= x
x
6 x 2 + 1 = 13
2
2
1
2 2
1
13
3 39
=
x
x
=
We cancelled the 4 with the two 2's
1
1
1 1
"I will earn $ 39 ."
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