Anatural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. some of the money is borrowed at 7%, some at 8.5%, and some at 9.5%. use a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. solve the system of linear equations using matrices.

Let the amount borrowed at 9.5% be x. Now we have:

at 9.5% = x

at 8.5% = 4x

at 7% = 2,000,000 - 5x

0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750

0.095x + 0.34x + 140,000 - 0.35x = 169,750

0.085x = 29,750

x = 350,000

So the museum borrowed:

At 9.5% = 350K

At 8.5% = 350*4 = 1,400,000

At 7% = 2,000,000 - 5(350,000) = 250,000

Total borrowed

350,000 + 1,400,000 + 250,000 = 2,000,000 Correct

Interest paid:

0.095(350,000) + 0.085(1,400,000) + 0.07(250,000) = 169,750

answer: in the short-run firms will respond by raising the price of turkey.

explanation: initially the long-run equilibrium is at a price of $5 per pound of turkey and a quantity of 50 million pounds per year. now, when webmd claims that a protein found in turkey will increase your expected lifespan by 4 years. the consumers demand for turkey will increase at every price shifting the demand curve to the right from d1 to d2. while, there will be no change in the supply curve in the short-run as it is not possible for producers to adjust supply so quickly. as a result the new equilibrium will occur at a higher price and a higher quantity of turkey.

thus, in the short run firms will respond by increasing the price of turkey, selling more quantity at a higher price and earning economic profits.