I04-19

Question

At the beginning of a given year, Sarah and Olivia each invested in two different mutual funds at simple annual interest rates of  x\%  and  y\% , respectively. Olivia invested  p  pounds, while Sarah invested 2,000 pounds less. By the end of the year, both earned the same total interest from their respective investments.
 
Select for  p  an expression for Olivia’s investment  p  in terms of x and y, and select for  x  an expression for Sarah’s interest rate  x  in terms of  p  and  y . Make exactly two selections, one from each column.

Bunuel · Answer

Official Solution:

Sarah's investment of  p-2,000  pounds in a year at at simple annual interest rates of  x\%  would earn  (p-2,000)*\frac{x}{100}  pounds
 
Olivia's investment of  p  pounds in a year at at simple annual interest rates of  y\%  would earn  p*\frac{y}{100}  pounds
 
Given that those earnings are equal, we'd have
   
 (p-2,000)*\frac{x}{100} =p*\frac{y}{100} 
 
 (p-2,000)x = py 
  
From this, for the second column, we get  x = \frac{py}{p-2,000} .
 
For the first column we get
  
 (p-2,000)x = py 
 
 px-2,000x = py 
 
 px-py=2,000x 
 
 p(x-y)=2,000x 
 
 p=\frac{2,000x}{x-y}

Correct answer:

p   " \frac{2,000x}{x-y} "

x   " \frac{py}{p-2,000} "

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Gouthamp114 · Answer