State University is planning a tuition raise. The Dean of Admissions suggests that they increase tuition by 10% each year for the next two years. The Provost suggests that each year they instead increase the tuition by 30% of the amount of the tuition above $10,000.

So, for example, if the tuition now is $25,000, the Dean of Admissions is suggesting a $2500 increase in the first year. Meanwhile, the Provost is suggesting a $4500 increase (since the current tuition is $15,000 more than $10,000, and 30% of $15,000 is $4500).

The Treasurer points out that the tuition two years from now (after two annual increases) will be the same under either the Dean's plan or the Provost's plan. What is the tuition right now? (Assume the tuition is not 0; State University is not free!)

Keihaku Feb 18, 2022

#2**+1 **

Percentages

Let's call X the original tuition, and let's assume it's greater than 10,000 so far. We'll analyze the first option:

Dean of Admissions suggests increasing tuition by 10% each year for the next two years. The first year the tuition would be. \(1.1x\)

The second-year the tuition would increase another 10% of the last amount, so it would end being. \(1.21x\)

Now for the second option:

The Provost suggests that each year they increase the tuition by 30% of the amount of the tuition above $10,000. The first increase would be \(0.3x-3000\)

And the new tuition at the end of the first year would be \(1.3x-3000\)

This new amount would be increased by applying the same rule, so the second-year increase would be 0.39x-3900

And the final tuition would be

1.69x - 6900

The Treasurer points out that the tuition will be the same under any scheme, so 1.69x - 6900= 1.21x

solve:

The actual tuition is $14,375

XxmathguyxX Feb 18, 2022

#1**+1 **

Write is as an equation, where \(x\) is the cost per year:

\(1.21x=1.3(x-10,000)\)

\(1.21x=1.3x-13,000\)

\(-0.09x=-13,000\)

\(0.09x=13,000\)

\(\color{brown}\boxed{144,444 {5 \over 9}}\)

A very expensive state college indeed :)

BuilderBoi Feb 18, 2022

#2**+1 **

Best Answer

Percentages

Let's call X the original tuition, and let's assume it's greater than 10,000 so far. We'll analyze the first option:

Dean of Admissions suggests increasing tuition by 10% each year for the next two years. The first year the tuition would be. \(1.1x\)

The second-year the tuition would increase another 10% of the last amount, so it would end being. \(1.21x\)

Now for the second option:

The Provost suggests that each year they increase the tuition by 30% of the amount of the tuition above $10,000. The first increase would be \(0.3x-3000\)

And the new tuition at the end of the first year would be \(1.3x-3000\)

This new amount would be increased by applying the same rule, so the second-year increase would be 0.39x-3900

And the final tuition would be

1.69x - 6900

The Treasurer points out that the tuition will be the same under any scheme, so 1.69x - 6900= 1.21x

solve:

The actual tuition is $14,375

XxmathguyxX Feb 18, 2022

#5**0 **

let's see what cphill gets.....

*getting so nervous*

*on the brink of extiction*

*super fast breathing*

XxmathguyxX Feb 18, 2022

#6**+1 **

Call T the tuition now

Under the Dean's plan the amount after two years can be expressed as T (1.10)^2 = 1.21T

The Provost's plan is a little trickier ..... T + ( T-10000).30 = 1.3T -3000 expresses the tuition after the first year

And [ 1.3T - 3000] + [1.3T -3000 - 10000].30 = 1.69T -6900 expresses the tution after the second

Set these equal

1.69T - 6900 = 1.21T

1.69 T - 1.21T = 6900

.48T = 6900

T= 14,375 = current tuition ( just as XxmathguyxX found !!! )

Proof

Dean Provost

After Year 1 15812. 50 15687.50

After Year 2 17393.75 17393.75

GREAT JOB, XxmathguyxX !!!!!

P.S - you can take a breath now.....

CPhill Feb 18, 2022

#7**+1 **

**THANK YOU CPHILL** for adding proof to my solution. Also thanks to @Builderboi for providing an answer. Thanks ya'll!

XxmathguyxX Feb 18, 2022