QUIZ 3 with Solutions

Define the variable(s) for each of the following problems.  Include the unit of measure for the variable(s), if applicable.

1.  One ton of an alloy that is 75% copper is to be obtained by fusing some alloy that is 60% copper and some other that is 81% copper.  How many pounds of each alloy must be used?

Let A = amt (lbs) of alloy with 60% copper, and B = amt (lbs) of alloy with 81% copper.

2.  If one solution is 10% acid and another 3.5%, how many cubic centimeters of each are needed to give 100 cubic centimeters of a solution that is 6% acid?

Let A = amt (cm3) of solution with 10% acid, and B = amt (cm3) of solution with 3.5% acid.

3. A firm mailed 140 letters, some requiring 3 cents postage and others 5 cents.  If the total bill is $4.60, find the number of letters mailed at each rate.

Let A = number of letters mailed with 3 cents postage, and B = number of letters mailed with 5 cents postage.

4. Two investments are made totaling $800.  Part of the money is invested at 8% and the rest at 9%.  In the first year, the total yield is $412 in simple interest.  Find the amount invested at each rate of interest.

Let A = amt ($) invested at 8%, and B = amt ($) invested at 9%.

5. Kahla paddled for 4 hr with a 6-km/h current to reach a campsite.  The return trip against the same current took 10 hr.  Find the speed of Kahla’s canoe in still water.

Let r = the speed of Kahla’s canoe in still water.

6. The perimeter of a rectangular ocean-front lot is 190 m.  The width is one-fourth of the length.  Find the dimensions.

Let L = the length of the rectangular lot, and W = the width of the rectangular lot.

7. In a triangle ABC, the measure of angle B is three times that of angle A.  The measure of angle C is 20 degrees more than that of angle A.  Find the angle measures.

Let A, B, and C be the angle measure of the angles in triangle ABC.

8. A collection of 43 coins consists of dimes and quarters.  The total value is $7.60.  How many dimes and how many quarters are there?

Let d = number of dimes, and q = number of quarters.

9. Two cars leave Salt Lake City, traveling in opposite directions.  One car travels at a speed of 80 km/h and the other at 96 km/h.  In how many hours will they be 528 km apart?

Let t = number of hours before the cars are 528 km apart.

10. Roscoe must play 12 commercials during his 1-hr radio show.  Each commercial is either 30 sec or 60 sec long.  If the total commercial time during that hour is 10 min, how many commercials of each type does Roscoe play?

Let A = number of 30 sec commercials, and B = number of 60 sec commercials.