<PRE><B>Question 185848</B>
Dave Salcedo has $40,000 to invest. He invests part of it at 5%, one-fourth
 of this amount at 6%, and the rest of the money at 7%. His total annual
 interest income is $2530. Find the amount invested at each rate.
:
We have 3 amts
let x = amt invested at 5%
then
.25x = amt invested at 6%
and
(40000-1.25x) = amt invested at 7%
:
.05x + .06(.25x) + .07(40000-1.25x) = 2530
:
.05x + .015x + 2800 - .0875x = 2530
:
.05x + .015x - .0875x = 2530 - 2800
:
-.0225x = -270
x = {{{(-270)/(-.0225)}}}
x = $12000 invested at 5%
:
.25(12000) = $3000 invested at 6%
and
40000 - 12000 - 3000 = $25000 invested at 7%
:
;
Check solution by finding the total interest
.05(12000) + .06(3000) + .07(25000) = 
600 + 180 + 1750 = 2530, confirms out solutions</PRE>