SOLUTION: A city government has approved the construction of a $800 million sports arena. Up to $480 million will be raised by selling bonds that pay simple interest at a rate of 4% annually

Question 646749: A city government has approved the construction of a $800 million sports arena. Up to $480 million will be raised by selling bonds that pay simple interest at a rate of 4% annually. The remaining amount (up to $640 million) will be obtained by borrowing money from an insurance company at a simple interest rate of 9%. Determine whether the arena can be financed so that the annual interest is $59 million. (If it is not possible, enter NONE for each answer.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x + y = 800
x <= 480
interest rate on x = .04
y <= 640
interest rate on y = .09
.04x + .09y = 59
x+y = 800
from x + y = 800, solve for y to get:
y = 800 - x
substitute for y in .04x + .09y = 59 to get
.04x + .09(800-x) = 59
simplify to get:
.04x + 72 - .09x = 59
combine like terms to get:
-.05x + 72 = 59
subtract 72 from both sides of the equation to get:
-.05x = -13
divide both sides of the equation by -.05 to get:
x = 260
this makes y = 540
you have:
x = 260
y = 540
x + y = 800
.04x + .09y = .04(260) + .09(540) = 10.4 + 48.6 = 59
that's your answer.
260 million raised at 4%
540 million raised at 9%.
total annual interest = 59 million.
interest is simple interest so the same amount of interest is payed out each year.

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