Question 112797
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?
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Let x = amt J invested at 12% and amt R invested at 10%
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Let y = amt J invested at 10% and amt R invested at 12%
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J's interest equation: .12x + .10y = 130
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R's interest equation: .10x + .12y = 134
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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
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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
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Check J's total interest
.12(500) + .10(700) =
   60     +   70 =  130
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Check R's total interest
.12(700) + .10(500) =
   84  +  50 = 134
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Did this make sense to you? Any questions?