Question 1184710
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%.