SOLUTION: Mr. B invested $250,000 in two different auto companies. the first earned a 5% profit and the second earned a 10% profit. If Mr. B made 3 times as much profit from the 10% investm

Question 1156795: Mr. B invested $250,000 in two different auto companies. the first earned a 5% profit and the second earned a 10% profit. If Mr. B made 3 times as much profit from the 10% investment as he did from the 5% investment how much did he invest in the company that made 5%?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if i did this correctly, then the answer should be 100,000 was invested in the 5% investment.
my reasoning is as follows.
let x = the 5% investment and let y = the 10% investment.
the profit on the 5% investment is .05 * x.
the profit on the 10% investment is .10 * y.
you are given that the profit on the 10% investment is 3 times as much as the profit from the 5% investment.
that means that .10 * y = 3 * .05 * x
simplify that equation to get .10 * y = .15 * x
solve for y to get y = .15 * x / .10.
simplify to get y = 1.5 * x.
since the total investment is 250,000, then x + y = 250,000, and if y = 1.5 * x, that equation becomes x + 1.5 * x = 250,000.
combine like terms to get 2.5 * x = 250,000.
solve for x to get x = 100,000.
that's your solution.
to go a step further, the 10% investment is equal to 150,000
.05 * 100,000 = 5,000
.10 * 150,000 = 15,000
the total profit is 20,000
the profit from the 10% investment is 3 times the profit from the 5% investment.
if you were not to solve this problem, knowing the total profit is 20,000, you would do the following.
x + y = 250,000
.05x + .10y = 20,000
multiply both sides of the first equation by .05 and leave the second equation as is to get:
.05x + .05y = 12,500
.05x + .10y = 20,000
subtract the first equation from the second to get .05y = 7,500.
solve for y to get y = 150,000.
that makes x = 100,000.
you went full circle, confirming the value of x and y are as stated in the original solution to this problem.
Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!

Mr. B invested $250,000 in two different auto companies. the first earned a 5% profit and the second earned a 10% profit. If Mr. B made 3 times as much profit from the 10% investment as he did from the 5% investment how much did he invest in the company that made 5%

Let amount invested in the 5% fund be F
Then amount invested in the 10% fund is: 250,000 - F
We then get the following EARNINGS equation: 3(.05F) = .1(250,000 - F)
.15F = 25,000 - .1F
.15F + .1F = 25,000
.25F = 25,000
Amount invested in the 5% fund, or
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