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Algebra
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I need help with this question a family has an annual income of $25,200. Of this, ¼ is spent for food, 1/5 for housing, 1/10 for clothing, 1/9 for savings, ¼ for taxes, and the rest for other expenses. How much is spent for other expenses?

Oct 23rd, 2014
I need help with this question a family has an annual income of $25,200. Of this, ¼ is spent for food, 1/5 for housing, 1/10 for clothing, 1/9 for savings, ¼ for taxes, and the rest for other expenses. How much is spent for other expenses?
to make the problem much easier we first outline how the money is spent
annual income : $25200
food: 1/4
housing: 1/5
clothing: 1/10
savings: 1/9
taxes: 1/4
expenses:the remainder
we need to find out how much this fractions represent
1/4 of $25200 = 25200/ 4 = $6300 is the actual amount of 1/4
$25200 - $6300 =$18900 is the remaining amount after the food expense was subtracted.So we now find out what 1/5 of 18900 is
1/5 of 18900 = 18900/ 5 =3780 we subtract this from 18900
18900 - 3780 =15120  we find out a tenth of this
1/ 10 of 15120
15120/ 10 = 1512we subtrct this from 15120 t get the reminder ot the total earnings
15120 - 1512 = 13608 we find what a ninth of this is
1/9 of 13608
13608/ 9 =1512 we subtract this from 13608 to get the remaining cash
13608 - 1512 =12096 we find a quarter f this
1/4 of 12096
12096/ 4=3024we subtract this from 12096 to get the remainder of the annul earnings
12096 - 3024 = 9072 this is the remaining amount after all the other expenses have been subtracted.It also is the amount spent on the rest of the expenses, thus we need to find a fraction of it.
we add all the fractions i.e 1/4 + 1/5 + 1/10 + 1/9 + 1/4 = 41/45
to get the total cost of 41/45 we  subtract 9072 which is the total remainder from the total annual salary i.e 25200 - 9072 = 16128
16128 is total cost of 41/45
we are told to find the fraction of  9072.To find it we do it this way:
41/45 =16128
  ?     = 9072
 to find the answer to our new problem we use cross multiplication i.e
 (41/45 x 9072)/ 16128
41 x 9072 = 371952/45
(371952/ 45)/ 16128
we need to eliminate the brackets in order to solve the sum we do it by making the 16128 a fraction i.e
(371952/ 45)/( 16128/ 1)
371952/ 45 x 1/ 16128 = 1/ 16 this is the answer to our problem.

 



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