SOLUTION: I need guidance on solving this problem. Kyle plans to invest $5500, part at 2% simple interest and the rest at 3% simple interest. What is the most he can invest at 2% and still

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Question 780820: I need guidance on solving this problem.
Kyle plans to invest $5500, part at 2% simple interest and the rest at 3% simple interest. What is the most he can invest at 2% and still be guaranteed at least $135 in interest per year?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Call x the amount invested at 3% and y at 2%. Then x+y = 5500.


The amount of interest earned for each investment is the amount invested times the interest rate. For x it's .03x and for y it's .02y, and their sum must be greater than or equal to $135.


.03x +.02y >= 135.


Solve the first equation for x: x = 5500-y. Substitute that into the second equation.
.03(5500-y) +.02y >= 135


165 - .03y + .02y >= 135


-.01y >= -30


y <= 3000


Check it: 3000*.02 + 2500*.03 = 60 + 75 = 135. The most he can invest at 2% is $3000.