Question

College increased the number of scholarships by 10% per year for each of the past two years. If 1815 scholarships will be offered this year, find the number offered two years ago.

Answer 1

The number of scholarships offered two years ago would be 1500 scholarships

Explanation:

Let us assume the number of scholarships two years ago to be X.

A 10% increase in a value means that the original value was multiplied by 110%. An example is this, 10% of 50 = 5. So, a 10% increase in 50 gives the new number (50+5), which is 55. We could also obtain it by directly multiplying 50 by 110% (that is 100% + the 10% increase).

50 × 110% = 50 ×
`(110)/(100)` = 55

So, back to the example that we are considering.

2 years ago: X scholarships

Last year at 10% increase per year will give: 110% × X = 1.1X

This year at another 10% increase, we have: 110% × 1.1X = 1.21X

Since we have been given the number of scholarships this year, we can equate it to 1.21X.

1.21X = 1815

X =
`(1815)/(1.21)`

X = 1500

So, the number of scholarships offered two years ago was 1500