Question

Dr. Blumen invested $5,000 part of it was invested in bonds at a rate of 6% in the rest was invested in a money market at the rate of 7.5% if the annual interest of is 337.50 how much did she invest in bonds

Answer 1

so... let's say the amounts invested were "a" at 6% and "b" at 7.5%.

ok.. hmm what's 6% of a? well, (6/100) * a or 0.06a.
what's 7.5% of b? well, (7.5/100) * b or 0.075b.

now... we know, whatever "a" and "b" are, they total the investment of 5000 bucks, thus a + b = 5000

and the interest yielded was 337.50, thus 0.06a + 0.075b = 337.50

thus    $\bf \begin{cases} a+b=5000\implies \boxed{b}=5000-a\\ 0.06a+0.075b=337.50\\ ----------\\ 0.06a+0.075\left( \boxed{5000-a} \right)=337.50 \end{cases}$

solve for "a", to see how much was invested at 6%.

what about "b"?  well, b = 5000 - a.

Answer 2

X = amount invested in bonds  (5000-X) = amount invested in money mkt
X (.06) + (5000-X)(.075) = 337.50
.06X + 375 - .075 X = 337.50
375 - 337.50 = .075 X - .06X
37.50 = .015 X
X = $2500 invested in bonds