Question

write an Algebraic equation for each problem and solve it. When necessary round your answer to the nearest tenth.
1. Health club membership in 2010, the number of Americans who were members of a health club was 45.3 million. This was an increase of 119% from the number of health club members in 1990. How many Americans were health club members in 1990?

Answer 1

I'm a little uncertain about the meaning of "increase of 119%". It could mean that the new number is 119% of the old number or that the difference between the new and old number equals 119% of the old number. Sorry, English is not my native language. Anyway, I'm going with the second interpretation.\[x(2010) = 45,3 \cdot 10^6\]\[x(2010) = x(1990) + 1,19\cdot x(1990)\]\[x(2010) = x(1990) \cdot (1 + 1,19) = 2,19\cdot x(1990)\]\[\Rightarrow x(1990) = \frac{x(2010)}{2,19} = \frac{45,3\cdot 10^6}{2,19} \approx 20,7 \cdot 10^6\] That means the answer would be 20,7 million.