Question 1009164
x = amount invested at 9.5%
y = amount invested at 12%


9.5% = .095
12% = .12


x + y = 54000


.095x + .12y = z


z = income


you are given that the income from the 12% investment is 3 times as large as the income from the 9.5% investment.


that leads to the following equation.


.12 * y = 3 * .095 * x


simplify to get:


.12 * y = .285 * x


divide both sides of the equation by .12 to get:


y = .285 * x / .12


simplify to get y = 2.375 * x


you know that x + y = 54000 and you know that y = 2.375 * x.


replace y with 2.375 * x and you get x + 2.375 * x = 54000.


simplify to get 3.375 * x = 54000.


divide both sides of that equation by 3.375 to get x = 16000.


since x + y = 54000, that means that y must be equal to 38000.


you get x + y = 54000 becomes 16000 + 38000 = 54000 which becomes 54000 = 54000 which confirms the value of x and y are good.


now go back to .095 * x  and replace x with 16000 to get .095 * 16000 to get 1520.


now go back to .12 * y and replace y with 38000 to get .12 * 38000 to get 4560


1520 is the income from the 9.5% investment.
4560 is the income from the 12% investment.


4560 / 1520 = 3.


the income from the 12% investment is 3 times the income from the 9.5% investment.


all the requirements of the problem have been satisfied.


your solution is that he invested 16000 at 9.5% and he invested 38000 at 12%.