EXERCISES 1.6 A. Solving equations

1. 9.

2. 10.

3. 11.

4. 12.

5. 13.

6. 14.

7. 15.

8. 16.

B. Solving inequalities

1. 10.

2. 11.

3. 12.

4. 13.

5. 14.

6. 15.

7. 16.

8. 17.

9.

C. Proving inequalities

1. If .

2. If .

3. If , show that the inequality is equivalent to .

D. Solving verbal problems 1. A group agrees to share equally in the cost of PhP 48,000 piece of machinery. If the group can find two

more members, each members share will decrease by Php 4000. How many are presently in the group?

2. A car radiator contains 10 liters of a 30% antifreeze solution. How many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?

3. Two cars start at a given time and travel in the same direction at average speeds of 40 kph and 55 kph.

How much time will elapse before the two cars are 10 km apart?

4. The demand equation for a hairbrush is , where x is the number of units demanded per day and p is the price unit. Find the demand if the price is set at Php29.95.

5. The tens digit of the number is 3 less than the units digit. If the number is divided by the sum of the

digits, the quotient is 4 and the remainder is 3. What is the original number?

6. A man can do certain job in 10 hours and his younger son can do it in 12 hours. After the father and his younger son have been working for 1 hour, the older son joins them, and the three completed the job in 3 more hours. How long will it take the older son to do the job alone?

7. Suppose you have P 8,000 invested at a certain rate of interest and P 6,000 at twice the first rate of

interest. The return from the first investment is P80 per year less than the return from the second. Find the interest rates.

8. A college rowing team can row 2 mi downstream in 8 min, but it takes 12 min for the team to row the

same distance upstream. How fast can the team row in still water, and what is the rate of the current?

9. A biologist introduces 200 ladybugs into a crop field. The population P of the ladybugs is

approximated by the model , where t is the time in days. Find the time required for

the population to increase to at least 2000 ladybugs.

10. The revenue for selling x units of a product is . The cost of producing x units is . To obtain a profit, the revenue must be greater than the cost. Determine the smallest

value of x for which this product returns a profit.

11. A ball is thrown upward with an initial velocity of 30 feet per second from a point that is 24 feet above the ground. The height h (in feet) of the ball at time t (in seconds) after the ball is thrown is

. Find the time when the ball hits the ground.

12. The side of a square is measured as 19.3 cm with possible error of 0.5 cm. Using these measurements, determine the interval containing the area of the square.