1. If $[latex]10,000[latex] is invested at a simple annual interest rate of [latex]6[latex] percent, what is the value of the investment after half a year?
2. To produce a particular radio model, it costs a manufacturer $[latex]30[latex] per radio, and it is assumed that if [latex]500[latex] radios are produced, all of them will be sold. What must be the selling price per radio to ensure that the profit (revenue from the sales minus the total production cost) on the [latex]500[latex] radios is greater than $[latex]8,200[latex] ?
3. Nancy purchased a consignment of [latex]c[latex] red roses at a cost of [latex]d[latex] dollars. She made bouquets with the roses and each bouquet contained [latex]d[latex] roses. She sold each bouquet at a price of [latex]c[latex] dollars. Overall, she made a profit.
| Quantity A | Quantity B |
| [latex]c[latex] | [latex]d[latex] |
4. If an amount [latex]P[latex] is to be invested at an annual interest rate of [latex]3.5[latex] percent, compounded annually, what should be the value of [latex]P[latex] so that the value of the investment is $[latex]1,000[latex] at the end of [latex]3[latex] years?
5. A college student expects to earn at least $[latex]1,000[latex] in interest on an initial investment of $[latex]20,000[latex]. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?
6. An antiques dealer bought c antique chairs for a total of [latex]x[latex] dollars. The dealer sold each chair for [latex]y[latex] dollars.
(a) Write an algebraic expression for the profit, [latex]P[latex], earned from buying and selling the chairs.
(b) Write an algebraic expression for the profit per chair.
7. A manufacturer sells goods at $[latex]4[latex] per unit to stockists after a [latex]10[latex]% profit. The stockists then sell the goods to distributors at [latex]25[latex]% profit. The distributor adds a [latex]20[latex]% profit on it and sells it to a retailer.
At what price (per unit) did the retailer purchase the goods?
(A) [latex]0.6[latex]
(B) [latex]6[latex]
(C) [latex]6.3[latex]
(D) [latex]6.6[latex]
(E) [latex]7[latex]
8. A manufacturer sells goods at $[latex]4[latex] per unit to stockists after a [latex]10[latex]% profit. The stockists then sell the goods to distributors at [latex]25[latex]% profit. The distributor adds a 20% profit on it and sells it to a retailer. If the retailer sells the goods to the end customer at [latex]10[latex]% profit, then what does each unit of the goods cost to a customer?
(A) [latex]4[latex]
(B) [latex]5[latex]
(C) [latex]6[latex]
(D) [latex]6.6[latex]
(E) [latex]7[latex]
9. A stockholder holds one share each of two different companies [latex]A[latex] and [latex]B[latex]. Last month, the value of a share of Company [latex]A[latex] increased by [latex]13[latex] dollars and that of Company [latex]B[latex] decreased by [latex]8[latex] dollars. How much did the net value of the two shares increase last month?
(A) [latex]2[latex]
(B) [latex]3[latex]
(C) [latex]4[latex]
(D) [latex]5[latex]
(E) [latex]6[latex]
10. A taxi driver makes $[latex]50[latex] an hour, but pays $[latex]100[latex] a day rent for his taxi and has other costs that amount to $[latex]0.50[latex] per mile. If he works three [latex]7[latex]-hour days and one [latex]9[latex]-hour day and drives a total of [latex]600[latex] miles in one week, what is his profit?
(A) [latex]700[latex]
(B) [latex]800[latex]
(C) [latex]1,100[latex]
(D) [latex]1,200[latex]
(E) [latex]1,500 [latex]
11. It costs a certain bicycle factory $[latex]11,000[latex] to operate for one month, plus $[latex]300[latex] for each bicycle produced during the month. Each of the bicycles sells for a retail price of $[latex]700[latex]. What is the minimum number of bicycles that the factory must sell in one month to make a profit?
(A) [latex]26[latex]
(B) [latex]27[latex]
(C) [latex]28[latex]
(D) [latex]29[latex]
(E) [latex]30[latex]
12. A clothing store bought a container of [latex]100[latex] shirts for $[latex]x[latex]. If the store sold all of the shirts at the same price for a total of $[latex]50[latex], what is the store’s profit per shirt, in dollars, in terms of [latex]x[latex]?
(A) [latex]50-\frac{ x }{ 100 }[latex]
(B) [latex]50-x[latex]
(C) [latex]5-x[latex]
(D) [latex].5-x[latex]
(E) [latex].5-\frac{ x }{ 100 }[latex]
13. Andrew sells vintage clothing at a flea market at which he pays $[latex]150[latex] per day to rent a table plus $[latex]10[latex] per hour to his assistant. He sells an average of $[latex]78[latex] worth of clothes per hour. Assuming no other costs, which of the functions below best represents profit per day [latex]P[latex] in terms of hours [latex]h[latex] that the flea market table is open for business?
(A) [latex] P(h) = 238-10h[latex]
(B) [latex]P(h) = 72-10h[latex]
(C) [latex]P(h) = 68h-150[latex]
(D) [latex]P(h) = 78h-160[latex]
(E) [latex]P(h) = -160h + 78[latex]
Answer:
1 $[latex]10,300[latex]
2 [latex]46.40[latex]
3 A
4 $[latex]901.94[latex]
5 [latex]4.91[latex] percent.
6 (a) [latex]P=cy-x[latex] (b) Profit per chair: [latex]\frac{ P }{ c }=\frac{ cy-x }{ c }=y-\frac{ x }{ c }[latex]
7 B
8 D
9 D
10 D
11 C
12 E
13 C
