Question around tax and percentages.

Question

A rare painting increased in value 3,100% over the past 49 years. This was an increase of $33,000. What was the value of the painting 49 years ago? What is the value of the painting now?

My answer key says these are the correct answers, however, I don't know the steps to solve the problem myself. Please help!

Answer Key:

The value of the painting 49 years ago was $1,064.52

The value of the painting now is $34,064.52

Answer 1

let x be the price of the painting 49 years ago, then the amount of increase is 3,100 %x or 31*x . recall that 100% = 1 so 3100% =31 times the original. we know the amount of increase is 33,000, so 31*x = 33,000. Divide both sides of equation by 31 and you obtain $1064.52. is the original price . To find the present price , you add 33,000 to the original price to get $34064.64.

Answer 2

33000 = 3100 % of x

33000 = 31.00x

1064.516129 = x