Question 1019123
it can't.


if the first part is invested at 10% and the second part is invested at 5%, the composite interest rate will be less than 10% unless the part that is invested at 5% is equal to 0.


you want a composite interest rate of 10%.
you invest x at 10%.
you invest y at 5%.


x + y = 45,000


.10*x + .05*y = .10 * (x + y)


simplify to get .10*x + .05*y = .10*x + .10*y


subtract .10*x and .10*y from both sides of the equation to get:


.10*x + .05*y - .10*x - .10*y = 0


combine like terms to get -.05*y = 0


solve fory to get y = 0.


since x + y = 45,000, and y = 0, then x must be equal to 45,000.


you must invest 0 at 5% and 45,000 at 10% to get a total of 45,000 at 10%.


so, the problem you posed is wrong because, in order for it to work, one of the parts must be greater than 10% and one of the parts must be less than 10%.


for example:


assume the first part is invested at 20% and the second part at 5% and you want the total to be invested at 10%.


you get:


x + y = 45,000
.20 * x + .05 * y = .10 * (x + y)


simplify the second equation to get:


.20 * x + .05 * y = .10 * x + .10 * y


subtract .10 * x and .10 * y from both sides of the equation to get:


.20 * x + .05 * y - .10 * x - .10 * y = 0


combine like terms to get .10 * x - .05 * y = 0


from x + y = 45,000, solve for y to get y = 45,000 - x


replace y with 45,000 - x in the equationn of .10 * x - .05 * y = 0 to get:


.10 * x - .05 * (45,000 - x) = 0


simplify to get .10 * x - 2250 + .05 * x = 0


combine like terms to get .15 * x - 2250 = 0


add 2250 to both sides to get .15 * x = 2250


divide both sides by .15 to get x = 2250/.15 = 15,000


since x + y = 45,000, then y = 45000 - 15000 = 30,000


you have 15,000 invested at 20% and 30,000 invested at 5%.


your total interest will be 3000 + 1500 = 4500.


4500 / 45,000 = 10%.


it works, but only if x is invested at greater than 10% and y is invested at less than 10%.