Question 1184710: A man invested part of P20,000 at 18% and the rest at 16%. The annual income from 16% investment was P620 less than three times the annual income from 18% investment. How much did he invest at 18%?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x equals the investment at 18%
y equals the investment at 16%
the annual income from the 16% investment is equal to 3 times the annual investment from the 18% income minus 620.
your two equations that need to be solved simultaneously are:
x + y = 20,000
.18x + .16y = .18x + 3 * .18x - 620
combine like terms to get:
x + y = 20,000
.18x + .16y = .72x - 620
subtract .72x from both sides of the second equation and leave the first equation as is to get:
x + y = 20,000
.18x - .72x + .16y = -620
combine like terms to get:
x + y = 20,000
-.54x + .16y = -620
multiply both sides of the first equation by .54 and leave the second equation as is to get:
.54x + .54y = 10,800
-.54x + .16y = -620
add both equations together to get:
.7y = 10180.
solve for y to get:
y = 10180 / .7 = 14,542.85714
solve for x to get:
x = 20,000 - y = 5,457.142857.
the interest on the value of x is equal to .18 * 5,457.142857 = 982.2857143.
the interest on the value of y is equal to .16 * 14,542.85714 = 2,326.857143.
multiply the interest on the value of x by 3 and subtract 620 from it to get:
3 * the interest on x - 620 = 3 * 982.2857143 -620 = 2326.857243.
solution looks good.
solution is:
he invested 5,457.142857 at 18%.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! A man invested part of P20,000 at 18% and the rest at 16%. The annual income from 16% investment was P620 less than three times the annual income from 18% investment. How much did he invest at 18%?
Let amount invested at 18% be E
Then amount invested at 16% = 20,000 - E
Income from 18% and 16% investments: .18E, and .16(20,000 - E), respectively
Based on what's given, we get: .16(20,000 - E) = 3(.18E) - 620
3,200 - .16E = .54E - 620
3,200 + 620 = .16E + .54E
3,820 = .7E
Amount invested at 18%, or 
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