Question 1009023
x = short range
y = intermediate range
z = long range.


x + y + z = 100,000


.05x + .06y + .07z = .0595 * 100,000 = 5950


x = y


replace y with x to get:


2x + z = 100,000
.11x + .07z = 5950


note that .11x is equivalent to .05*x + .06*x.


multiply both sides of the second equation by 100 and multiply both sides of the first equation by 7 to get:


14x + 7z = 700,000
11x + 7z = 595,000


subtract second equation from the first to get:


3x = 105,000


solve for x to get:


x = 35,000


in the first original equation of 2x + z = 100,000, replace x with 35,000 to get 2 * 35,000 + z = 100,000.


this becomes 70,000 + z = 100,000.


solve for z to get z = 30,000


in the second original equation of .11x + .07z = 5950, replace x with 35,000 and replace z with 30,000 to get .11 * 35,000 + .07 * 30,000 = 5950.


simplify to get 5950 = 5950.


this confirms the solution is correct.


.11 * x is equivalent to .05 * x + .06 * x


since y = x, this is equivalent to .05 * x + .06 * y 


both x and y are equal to 35,000, so this is equivalent to .05 * 35,000 + .06 * 35,000.


you have:


.05 * 35,000 dollars in short term bonds + .06 * 35,000 in intermediate term bonds + .07 * 30,000 dollars in long term bonds.


the total money invested is 100,000.


the total interest earned is 5,950


5,950 / 100,000 = .0595


.0595 * 100 = 5.95%.