Question 1153600

Mr. Thorpe inherited a sum of money. He invested 2/5 of this sum at 6%, 1/3 at 5%, and the rest at 8%. If the annual income from these investments was $2790, find the amount of money he inherited.
<pre>Fraction invested at 8%: {{{matrix(1,5, 1 - (2/5) - (1/3), "=", 15/15 - 6/15 - 5/15, "=", 4/15)}}} 
Let amount be A
Then we get: {{{matrix(2,3, .06(2/5)A + .05(1/3)A + .08(4/15)A, "=", "2,790", 
.12A/5 + .05A/3 + .32A/15, "=", "2,790")}}}
3(.12A) + 5(.05A) + .32A = 41,850 ------- Multiplying by LCD, 15
.36A + .25A + .32A = 41,850
.93A = 41,850
A, or amount inherited = {{{highlight_green(matrix(1,3, "41,850"/.93, "=", "$45,000"))}}}