Question 1092288: In 2020 a city's budget is projected to be $37 million. This is approximately 15/11 of the 2000 budget. What was the city's budget in 2000?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in 2020, the city's budget is 37 million.
this is 15/11 of the 2000 budget.
let x equal the 2000 budget.
then the 2020 budget is equal to 15/11 * x.
if the 2020 budget is equal to 37 million, then 37 million is equal to 15/11 * x
your equation is 37 = 15/11 * x
multiply both sides of this equation by 11/15 and you get 11/15 * 37 = 11/15 * 15/11 * x
11/15 * 37 is equal to 27.13333333..... which is equal to 407/15 which is equal to 27 + 2/15.
11/15 * 15/11 is equal to 1.
equation becomes
27 + 2/15 = 1 * x which becomes 27 + 2/15 = x.
the 2000 budget was 27 + 2/15 million, or approximately 27.13 million rounded to 2 decimal digits.
if you take 27 + 2/15 and multiply it by 15/11, you will get (27 + 2/15) * 15/11 equals 27 * 15/11 + 2/15 * 15/11 which is equal to 405/11 + 2/11 which is equal to 407/11 which is equal to 37.
solution checks out.
the 2000 budget was 27 + 2/15, or 27.13 rounded to 2 decimal digits.
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