Question 1168300
your equation is 1520 = .05 * x + .07 * y + .08 * z


x is the amount invested at 5%
y is the amount invested at 7%
z is the amount invested at 8%.


you are given that the amount invested at 5% is half the amount invested at 7%.


this makes x = .5 * y.


you are given that the amount invested at 7% is 1500 less than the amount invested at 8%.


this makes y = z - 1500.


solve for z in the equation of y = z - 1500 to get z = y + 1500.


you have x = .5 * y and z = y + 1500.


in the equation of 1520 = .05 * x + .07 * y + .08 * z, replace x with .5 * y and replace z with y + 1500 to get:


1520 = .05 * .5 * y + .07 * y + .08 * (y + 1500)


simplify to get 1520 = .025 * y + .07 * y + .08 * y + .08 * 1500


since .08 * 1500 = 120, then the equation becomes:


1520 = .025 * y + .07 * y + .08 * y + 120


subtract 120 from both sides of the equation to get:


1520 - 120 = .025 * y + .07 * y + .08 * y


simplify and combine like terms to get:


1400 = .175 * y


solve for y to get:


y = 8000.


when y = 8000, x = .5 * y = 4000 and z = y + 1500 = 9500


you get x = 4000, y = 8000, z = 9500


your original equation of 1520 = .05 * x + .07 * y + .08 * z becomes:


1520 = .05 * 4000 + .07 * 8000 + .08 * 9500


simplify to get 1520 = 1520.


this confirms the values of x and y and z are good.


the amount invested at 5% is 4000
the amount invested at 7% is 8000
the amount invested at 8% is 9500


that's your solution.


the amount invested at 5% is half the amount invested at 7%.
the amount invested at 7% is 1500 less than the amount invested at 8%.


the requirements of the problem have been satisfied, so the solution is good.