Word Problems — Quiz 12

Questions in this quiz (10)

1. The price of a gallon of milk is currently $$2.80$$ dollars, and the price of a loaf of bread is $$4.90$$ dollars. The price of milk increases at a constant rate of $$4x$$ cents per day, and the price of bread decreases at a constant rate of $$\sqrt{3x} - x$$ cents per day. What is the approximate price when the gallon of milk costs the same as the loaf of bread?

   • 2.80
   • 2.10
   • 4.97
   • 5.25

2. A and B ran a race of 480 meters. In the first heat, A gives B a head start of 48 meters and beats him by $$\frac{1}{10}$$ minute. In the second heat, A gives B a head start of 144 meters and is beaten by $$\frac{1}{30}$$ minute. What is B's speed in meters per second?

   • 14
   • 15
   • 16
   • 12

3. A certain quantity of 40 percent solution is replaced with 25 percent solution such that the new concentration is 35 percent. What is the fraction of the solution that was replaced?

   • $$\frac{2}{3}$$
   • $$\frac{1}{3}$$
   • $$\frac{1}{4}$$
   • $$\frac{3}{4}$$

4. A bag contains 3 red, 4 black, and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

   • $$\frac{2}{27}$$
   • $$\frac{1}{3}$$
   • $$\frac{4}{27}$$
   • $$\frac{2}{9}$$

5. For a certain company, operating costs and commissions totaled 550 million dollars in 1990, representing an increase of 10 percent from the previous year. The sum of operating costs and commissions for both years was what?

   • $$1100$$
   • $$1050$$
   • $$1250$$
   • $$1000$$

6. Fox jeans regularly sell for 15 dollars a pair and Pony jeans regularly sell for 18 dollars a pair. During a sale these regular unit prices are discounted at different rates so that a total of 9 dollars is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?

   • $$12%$$
   • $$10%$$
   • $$15%$$
   • $$13%$$

7. If 75 percent of a class answered the 1st question on a certain test correctly, 55 percent answered the 2nd question on the test correctly and 20 percent answered neither of the questions correctly, what percent answered both correctly?

   • $$50\%$$
   • $$45\%$$
   • $$40\%$$
   • $$35\%$$

8. A merchant sells an item at a 20 percent discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

   • $$50\%$$
   • $$75\%$$
   • $$65\%$$
   • $$72.5\%$$

9. The list of numbers 50, 42, 28, A, B, 10 has a median of 30. The mode of the list is 10. To the nearest whole number, what is the mean of the list?

   • 26
   • 27
   • 28
   • 29

10. You are given the system of equations:$$y = x^2$$$$ax + by = c$$where $$a$$, $$b$$, and $$c$$ are integers.For which of the following conditions will the system have more than one real-number $$(x,y)$$ solution?

    • $$b^2$$ - 4ac > $$0$$
    • $$b^2 - 4ac \le 0$$
    • $$a^2$$ + 4bc > $$0$$
    • $$a^2 + 4bc = 0$$