Question

The board of trustees for a school is considering a tuition increase. One faction in the board supports Plan​ A, which involves raising the tuition 9​% this year and 8​% the next. Others want Plan​ B, which has the 8​% raise this year and the 9​% next year. Some say it​ doesn't matter because in either​ case, the tuition is the same in the second year. Does it make any difference as to which plan is​ implemented?

Answer 1

It doesn't matter which plan is implemented. In either case, the tuition will be same.

Explanation:

Let current tuition fee be
`x`

Plan A:

Raise 9% first year:
`x+(0.09)x=1.09x`

Raise 8% 2nd year:
`1.09x+(0.08)(1.09x)=1.1772x`

Plan B:

Raise 8% first year:
`x+(0.08)(x)=1.08x`

Raise 9% 2nd year:
`1.08x+(0.09)(1.08x)=1.1772x`

As we can see, the amount is same for BOTH THE PLANS. So it doesn't matter which plan in implemented.