SOLUTION: If Ben invests $4000 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that the interest he receives each year is 4 1/2% of the

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Question 262662: If Ben invests $4000 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that the interest he receives each year is 4 1/2% of the total amount invested? How would I set that up algebraically to solve?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the additional money he has to invest at 5.5% interest.

your equation is:

.04 * 4000 + .055 * x = .045 * (4000+x)

simplify to get:

160 + .055*x = .045 * (4000 + x)

simplify further to get:

160 + .055*x = (.045 * 4000) + (.045 * x)

simplify further to get:

160 + .055*x = 180 + .045*x

subtract .045*x from both sides of the equation and subtract 160 from both sides of the equation to get:

.055*x - .045*x = 180 - 160

simplify to get:

.01*x = 20

divide both sides of the equation by .01 to get:

x = 2000.

replace x by 2000 in the original equation to confirm the answer is good.

original equation is:

.04 * 4000 + .055 * x = .045 * (4000+x)

substitute 2000 for x to get:

.04 * 4000 + .055 * 2000 = .045 * 6000

simplify to get:

160 + 110 = 270

simplify further to get:

270 = 270 which is true, confirming that the value for x is good.

your answer is:

the additional money that he has to invest at 5.5% is $2,000.