SOLUTION: 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

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(10551) (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
RELATED QUESTIONS
A man invested part of P10, 000 at 6% and the rest at 7%. The annual income from the 7%... (answered by ikleyn)
A man invested part of 10,000 @ 6% and the rest @ 7%. The annual income from the 7% was... (answered by fractalier)
Mr. Dunnn invested $35,000 part at 8% and the rest at 5%. His anual income from the 8%... (answered by ankor@dixie-net.com)
A man invested part of $10,000 at 6% and rest at 7%. The annual income from 7% invested... (answered by stanbon)
Here is the question: A man has $8000 invested, part at 4% and the rest at 2.5%. The... (answered by ewatrrr)
Investment Problem A man invested Php 6,000, part of it at 3% and the rest at 4%. The... (answered by Boreal,greenestamps)
The sum of $4000 is invested, part at 4% and the rest at 6%. The annual income from the... (answered by greenestamps)
a man invested $25,000, part of it was invested at 3% and the rest at 4%. the total... (answered by checkley77)
a man invested $25,000, part of it was invested at 3% and the rest at 4%. the total... (answered by checkley77)