Question 1173936: please help me solve this problem: peter invested P300000.00 with 15% return in an electronic shop and 8% return in real estate. his annual income from his investments is P40000.00. how much did he invest in the electronics shop?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! his total investment was 300,000.
let x = the investment in the electronic shop and y equal the investment in real estate.
first equation is x + y = 300,000.
second equation is .15x + .08y = 40,000.
first equation tells you the amount invested.
second equation tells you the interest on the investment.
these two equations need to be solved simultaneously.
they are:
x + y = 300,000
.15x + .08y = 40,000
multiply both sides of the first equation by .15 and leave the second equation as is to get:
.15x + .15y = 45,000
.15x + .08y = 40,000
subtract the second equation from the first to get:
.07y = 5,000
solve for y to get:
y = 5,000 / .07 = 71,428.57143
solve for x to get:
x = 300,000 - 71,428.57143 = 228,571.4286.
replace the two original equations with these values for x and y to get:
x + y = 228,571.4286 + 71,428.57143 = 300,000
.15x + .08y = .15 * 228,571.4286 + .08 * 71,428.57143 = 40,000.
this confirms the solution is correct.
the solution is that he invested 228,571.4286 in the electronics shop.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a non-algebraic way to solve any two-part mixture problem like this.
The fraction of the mixture that is each investment is determined by where the average return rate lies between the return rates of the two investments.
(1) P40,000 return on an investment of P300,000 is a rate of 40,000/300,000 = 4/30 = 13 1/3%.
(2) Consider the three percentages 8, 13 1/3, and 15 on a number line. Perform calculations to find that the 13 1/3% is (5 1/3)/7 = 16/21 of the way from 8% to 15%.
(3) That means 16/21 of the investment was at the higher rate, so 5/21 was at the lower rate.
ANSWER: 16/21 of the total P300,000, or P228,571 (rounded) was invested in the electronics shop.
Note that, technically, the problem can't be solved with the exact given information, since that information produces answers that are not whole numbers....
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