# A stationery company discovers

August 30, 2017

Question
Finite Math 105

1. A stationery company discovers the following information: At a price of \$5 they can sell 30 boxes of stationery. At a price of \$10 they can sell 15 boxes. Find the price-demand equation assuming it’s linear.

2. The company in problem 1 discovers that they can supply 10 boxes if they cost \$5 each and they can supply 20 boxes if they cost \$10 each. Find the price-supply equation assuming it’s linear.

3. Sketch both lines from problems 1 and 2 on the same set axes.

4. Determine the equilibrium price and the equilibrium number of the boxes for the stationery company in the previous problem.

5. Suppose one car rental company charges \$15 per day plus \$0.20 per mile while a second one charges \$25 per day plus \$0.15 per mile. Answer each of the following questions assuming you only plan on renting the car for one day:

a) Give an expression for the total cost of driving x miles if we rent from the first agency.

b) Give an expression for the total cost of driving x miles if we rent from the second agency.

c) If we’re only going to drive 100 miles, which agency should we choose?

d) For what distance will the two agencies charge the same amount?

6. If \$5000 is loaned for 9 months at a 6.2% annual rate, how much interest is earned?

7. What is the purchase price of a 26-week T-bill with a maturity value of %1,000 that earns an annual interest rate will of 4.903%?

8. In a suburb, housing costs have been increasing at 5.2% per year compounded annually for the past 8 years. A house worth \$260,000 now would have had what value 8 years ago?

9. If you deposit \$10,000 in a savings account now, what rate compounded continuously would be required for you to withdraw \$12,500 at the end of 4 years?

10. USG Annuity and Life offered an annuity that pays 7.25% compounded monthly. If \$1,000 is deposited into this annuity every month, how much is in the account after 15 year? How much of this is interest?

11. The total number of nickels, dimes, and quarters in a box is 900. There are 20 more nickels than there are dimes. The number of nickels and dimes together is 44 more than the number of quarters. How many coins of each denomination are there? How much money is in the box?

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