SOLUTION: Juan invests $250,000 in two accounts. Juan would like to earn $7700 a year to pay some expenses. Juan invests part of the money in an account paying 3% simple interest and the res

Question 799803: Juan invests $250,000 in two accounts. Juan would like to earn $7700 a year to pay some expenses. Juan invests part of the money in an account paying 3% simple interest and the rest in an account paying 4% simple interest.
(a) What variables are appropriate?
(b) Write a system of equations that will help Juan find the amount that should be invested in each account.
()Total amount invested

()Total interest earned

(c) How much does Juan need to invest in each account to earn $7700 per year? (Include units with your numerical answers.)
Juan needs to invest in the account paying 3% interest and in the account paying 4% interest.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Juan invests $250,000 in two accounts. Juan would like to earn $7700 a year to pay some expenses. Juan invests part of the money in an account paying 3% simple interest and the rest in an account paying 4% simple interest.

(a) What variables are appropriate?
(b) Write a system of equations that will help Juan find the amount that should be invested in each account.
Amount Equation:: x + y = 250,000
Interest Equation: 0.03x + 0.04y = 7700
--------------------------------------------
(c) How much does Juan need to invest in each account to earn $7700 per year? (Include units with your numerical answers.)
Modify for elimination::
3x +3y = 3*250,000
3x +4y = 770000
-----------------------
Subtract and solve for "y":
y = 20,000 (amt. invested at 4%)
--------------
x = 230,000 (amt. invested at 3%)
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Cheers,
Stan H.
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Juan needs to invest in the account paying 3% interest and in the account paying 4% interest.
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Cheers,
Stan H.

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