SOLUTION: Jane invested some amount at the rate of 12% simple interset and some other amount at the rate of 10% simple interest. She recieved yearly interset of $130. Randy also invested in

Question 112797: Jane invested some amount at the rate of 12% simple interset and some other amount at the rate of 10% simple interest. She recieved yearly interset of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and recieved $4 more as interest. How muchamount did each of them invest at different rates?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?
:
Let x = amt J invested at 12% and amt R invested at 10%
:
Let y = amt J invested at 10% and amt R invested at 12%
:
J's interest equation: .12x + .10y = 130
:
R's interest equation: .10x + .12y = 134
:
Multiply J's equation by 1.2 and subtract R's equation:
.144x + .12y = 156
.10x + .12y = 134
------------------subtracting eliminates y
.044x + 0y = 22
x = 22/.044
x = $500 invested at 12% by J and 10% by R
:
Find y using .10x + .12y = 134; (.10(500) = $50)
50 + .12y = 134
.12y = 134 - 50
.12y = 84
y = 84/.12
y = $700 invested at 10% by J and 12% by R
:
Check J's total interest
.12(500) + .10(700) =
60 + 70 = 130
:
Check R's total interest
.12(700) + .10(500) =
84 + 50 = 134
:
:
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