Question

Table

Food - 1/3
Housing - 1/3
Medical Care - 1/4

This year, the managers of the farm will change the fraction of the budget for housing to 1/8 but will leave the fraction of the budget for food and medical Care the same. Again, the remaining portion of the budget will be for maintenance expenses. What is the difference between the fraction of the budget for maintenance this year and last year?

Answer 1

Before budget change :

Maintenance = 1 - 1/3 - 1/3 - 1/4 = 1/12

After budget change :

Maintenance = 1 - 1/3 - 1/8 - 1/4 = 7/24

Difference in budget for maintenance = 7/24 - 1/12 = 5/12

Answer 2

`(5)/(24)`

Explanation:

Previous year table .

Food -
`(1)/(3)`

Housing -
`(1)/(3)`

Medical Care -
`(1)/(4)`

So, total =
`(1)/(3)+(1)/(3)+(1)/(4)`=
`(11)/(12)`

Since we are given that the remaining portion of the budget will be for maintenance expenses.

So, maintenance expenses =

Present year table

Food -
`(1)/(3)`

Housing -
`(1)/(8)`

Medical Care -
`(1)/(4)`

So, total =
`(1)/(3)+(1)/(8)+(1)/(4)=(17)/(24)`

Since we are given that the remaining portion of the budget will be for maintenance expenses.
`1-(17)/(24)=(7)/(24)`

The difference between the fraction of the budget for maintenance this year and last year = 7/24 - 1/12 = 5/24

Hence the difference between the fraction of the budget for maintenance this year and last year is 5/24