Respuesta :
Given:
The first fund earns $600 and the second fund earns $800.
Let x% be the lower rate of interest.
And x+4% be the higher rate of interest.
The difference between the amounts is,
[tex]800-600=200[/tex]It means,
[tex]\begin{gathered} 4\text{ percent of n =200} \\ \text{Where n is the amount invested. } \\ \frac{4}{100}\times n=200 \\ n=\frac{200\times100}{4} \\ n=5000 \\ It\text{ gives } \\ \text{x percent of }5000=600 \\ \frac{x}{100}\times5000=600 \\ x=\frac{600}{50} \\ x=12 \\ \text{Same way,} \\ \text{x percent of }5000=800 \\ \frac{x}{100}\times5000=800 \\ x=\frac{800}{50} \\ x=16 \end{gathered}[/tex]Alternative way,
For the first fund. let a be the lower rate and a+4 be the higher rate.
[tex]ax=600[/tex]For second fund,
[tex]\begin{gathered} x(a+4)=800 \\ ax+4x=800 \\ 600+4x=800 \\ 4x=800-600 \\ x=\frac{200}{4} \\ x=50 \end{gathered}[/tex]So,
[tex]\begin{gathered} ax=600 \\ 50a=600 \\ a=\frac{600}{50} \\ a=12 \\ \Rightarrow a+4=12+4=16 \end{gathered}[/tex]Answer: The lower rate of interest is 12%
