How much was raised two years ago if the amount this year is 10120 and this year was 15 percent greater than last year and that was 10 percent greater than 2 years ago?

Answer 1

Let the amount 2 years ago be y

Let the amount last year be z.

The last year, the amount raised being 10 % greater was y + 10% of y;

This is the same as 100 % of y + 10% of y, a total of 110% of y

Percent means "out of 100" so 110% = 110/100 = 1.1, meaning last year was

this is the same as 100% of y + 10% of y = 110% of y which is 110/100 y = 1.1y

→ z = 1.1y

This year the amount raised is 15 % greater than last year, ie it is z + 15% of z

This is the same as 100% of z + 15% of z = 115% of z

This is the same as 115/100 z = 1.15z

But z = 1.1y, thus the amount raise this year is 1.15 × 1.1y = 1.265y

The amount raised this year is given as 10120, which means:

1.265y = 10120

→ y = 10120 ÷ 1.265 = 8000

Checking this:

Last year is 10% greater giving 8000 × 1.1 = 8800

This year is 15% greater giving 8800 × 1.15 = 10120

Answer 2

The "multiplier" for an R percent change is M = (1 + R/100), where R is positive for an icrease and negative for a decrease. When going forward in time, you multiply by M and when going back in time you divide by M.

So, the answer is (10120/1.15)/1.10 = 8800/1.10 = 8000.