<PRE><B>Question 262662</B>
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.






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