# SOLUTION: I don't understand how to set up this problem in order to solve it because the book examples do not break it up the same way. Dave invested half his money at 5%, one-third his mon

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 Question 160678: I don't understand how to set up this problem in order to solve it because the book examples do not break it up the same way. Dave invested half his money at 5%, one-third his money at 4%, and the rest of his money at 3.5%. If his total annual investment income was \$530, how much had he invested?Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!first thing you have to do is find out what the rest is. several ways to do it. one way is as follows: 1/2 + 1/3 + x = 1 solve for x. easiest way is to multiply both sides of the equation by 6 to remove the denominators. equation becomes 3 + 2 + 6*x = 6 6*x = 6 - 3 - 2 = 1 x = 1/6 ----- to see if that's correct, add up 1/2 + 1/3 + 1/6 to see if it adds up to 1. 1/3 is the same as 2/6. 1/2 is the same as 3/6 so 2/6 + 3/6 + 1/6 = 6/6 = 1. x = 1/6 is good. ----- you know what the total income each year is. it's \$530. ----- now you know that: 1/2 of the money is invested at 5%. 1/3 of the money is invested at 4%. 1/6 of the money is invested at 3.5% ----- if 1/2 of the money is invested at 5%, then the amount of income from 1/2 of the money at the end of the year is 5% times (1/2 of the money). this also means that 4% times (1/3 of the money) give you the amount of income from 1/3 of the money at the end of the year. this also means that 3.5% times (1/6) of the money) gives you the amount of income from 1/6 of the money ----- let y = total amount of money invested. let \$530 = total income from money invested. equation becomes: 5%*y*1/2 + 4%*y*1/3 + 3.5%*y*1/6 = \$530 ----- this is the same as (5%*y)/2 + (4%*y)/3 + (3.5%*y)/6 = \$530. ----- to get the interest rate you have to divide by 100%. 5% / 100% = .05 4% / 100% = .04 3.5% / 100% = .035 ----- you substitute interest rate for % interest and the equation becomes ----- (.05*y)/2 + (.04*y)/3 + (.035*y)/6 = \$530. multiplying both sides of the equation by 6 to remove the denominators, and the equation becomes 3*.05*y + 2*.04*y + .035*y = 6*\$530 which becomes .15*y + .08*y + .035*y = \$3180 which becomes .265*y = \$3180 which becomes y = \$3180/.265 which equals \$12000. ----- to prove that the answer is correct, you substitute \$12000 for y and solve the original equation after you converted from % to rate. that equation is .05*y*(1/2) + .04*y*(1/3) + .035*y*(1/6) = \$530. which becomes .05*12000*(1/2) + .04*12000*(1/3) + .035*12000*(1/6) = \$530. which becomes \$300 + \$160 + \$70 = \$530 which becomes \$530 = \$530 which proves the equation is good. ----- your answer is total money invested is \$12000.