SOLUTION: the annual interest on a $19000 exceeds the investment exceeds the interest earned on a $6000 investment by $1154. the $19000 interest is invested at a 0.6% higher rate than the $6

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Question 897287: the annual interest on a $19000 exceeds the investment exceeds the interest earned on a $6000 investment by $1154. the $19000 interest is invested at a 0.6% higher rate than the $6000. what is the interest rate of each investment
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the interest rate on the 19000 investment.
let y equal the interest rate on the 6000 investment.

the interest on the 19000 investment is equal to x * 19000
the interest on the 6000 investment is equal to y * 6000

the interest on 19000 exceeds the interest on 6000 by 1154.
formula for that becomes:
19000*x = 6000*y + 1154

the interest rate percent on the 19000 investment is 0.6% higher than the interest rate on the 6000 investment.
formula for that becomes:
x = y + .006
this is because interest rate is equal to interest rate percent divided by 100.
.6% becomes .006.

you have 2 equations.
they are:

19000*x = 6000*y + 1154
x = y + .006

replace x in the first equation with y + .006 from the second equation to get:
19000*(y+.006) = 6000*y + 1154

now you can solve for y.

simplify the equation to get:
19000*y + 19000*.006 = 6000*y + 1154
simplify to get:
19000*y + 114 = 6000*y + 1154
subtract 6000*y from both sides of the equation and subtract 114 from both sides of the equation to get:
19000*y - 6000*y = 1154 - 114
simplify to get:
13000*y = 1040
divide both sides of the equation by 19000 to get:
y = 1040/19000
simplify to get:
y = .08

since x = y + .006, then you get:

y = .08
x = .086

those are your answers.
all you need to do is confirm they are correct.

go back to your original equation of 19000*x = 6000*y + 1154 and replace x with .086 and replace y with .08 and then solve.

you get 19000*.086 = 6000*.08 + 1154
simplify to get:
1634 = 1634
this confirms the solution is correct.

your solution is:

interest rate on the 19000 investment is 8.6%
interest rate on the 6000 investment is 8.0%

the interest rate on the 19000 investment is .6% greater than the interest rate on the 6000 investment.
the interest on the 1900 investment is 1154 greater than the interest on the 6000 investment.

all is good.