Question

Mr. Jones invested a sum of money in 6% bonds. He invested $400 more than this sum in 4% bonds. If his total annual income was $116, how much did he invest in each kind of bond?

Answer 1

a = amount invested at 6%

how much is 6% of "a"? (6/100) * "a", namely 0.06a.

b = amount invested at 4%

how much is 4% of "b"? (4/100) * "b", namely 0.04b.

we also know that the yielded amount in interest or the annual income he's got from both is $116, so if we simply add their interest, that'd be 0.06a + 0.04b = 116.

We also know that he invested 400 more in "b" than in "a", so whatever "a" might be, we know that b = a + 400.

`0.06a~~ + ~~0.04(\stackrel{b}{a+400})~~ = ~~116\implies 0.06a+0.04a+16=116 \\\\\\ 0.10a+16=116\implies 0.10a=100\implies a=\cfrac{100}{0.10} \\\\\\ \boxed{a=1000}\hspace{5em}\stackrel{1000+400}{\boxed{b=1400}}`