Honors Algebra 2: §1.9 Word Problems

  1. The manager of a soccer team bought 4 pieces of artificial turf to cover the entire 100 m\(^2\) area of the soccer pitch. Three of the pieces each cover 20 m\(^2\) less in area than the fourth piece covers. How much area did each piece of artificial turf cover?
  2. Solution \( \displaystyle \{ 20, 20, 20, 40 \} \)
  3. Caryn and Jeff start out from towns 164 km apart and drive toward each other. Jeff travels at a rate of 40 km/hr and Caryn travels at a rate of 48 km/hr. If Caryn begins the trip 15 minutes after Jeff does, how long after Jeff leaves will they meet?
  4. Solution 2 hours
  5. The length of one base of a trapezoid is three times the length of the other base. The height of the trapezoid is 12 cm and its area is 120 cm\(^2\). What are the lengths of the bases? (Common geometric formulas can be found in the appendix of the book.)
  6. Solution \( \{ 5, 15 \} \)
  7. A bus left City A at 9:00 am and headed toward City B at 50 mph. A car left city B at 10:00 am and traveled toward City A at 40 mph. When did the busses meet if the cities are 230 miles apart?
  8. Solution noon
  9. David began a marathon run at 6:30 am and averaged 12 km/h while Beth began the run at 7:00 am and averaged 15 km/hr. At what time did Beth pass David?
  10. Solution 9:00 am
  11. Some 20 cent birthday cards and some 35 cent birthday cards are mixed to make a package of 40 cards. How many cards of each kind are needed to make a package worth $10.25?
  12. Solution \( \displaystyle \{25, 15\} \)
  13. Mrs. Goff is 26 years older than her son. Ten years ago, she was 3 times as old as he was. How old is each one now?
  14. Solution \( \displaystyle \{49, 23\} \)
  15. Find three consecutive multiples of 5 so that 4 times the second number is the same as 190 decreased by twice the third.
  16. Solution \( \displaystyle \{25, 30, 35\} \)
  17. Find three consecutive odd integers so that 5 times the second, decreased by twice the third, is -20 more than the first.
  18. Solution \( \displaystyle \{-11, -9, -7\} \)
  19. Side \(b\) of a triangle is 4 cm longer than side \(a\), and 6 cm shorter than side \(c\). Find the length of each side if the perimeter is 80 cm.
  20. Solution \( \displaystyle \{22, 26, 32 \} \)
  21. Corn worth 20 cents per kg is mixed with oats worth 30 cents per kg. There are 40 kg more oats than corn. How many kg of oats are used if the mixture is worth $32.00?
  22. Solution 80 kg
  23. A man traveled 150 miles at a certain average rate. By increasing his average rate by 20 mph, he traveled 250 miles in the same time that he spent on the 150 mile trip. Find his average rate on the first trip.
  24. Solution 30 mph
  25. An angle whose degree measure is 120\(^o\) is divided into three angles with ratio 2:3:7. Find the degree measure of each angle.
  26. Solution \( \displaystyle \{20, 30, 70\} \)
  27. Your friend at college lives 164 km away. You plan to meet one afternoon by traveling toward each other. If you leave at 2:00 pm and go at a rate of 40 km/h and your friend leaves at 2:15 pm and travels at 48 km/h, at what time will you meet, and how far will each of you have traveled?
  28. Solution 4:00 pm; 80 km and 84 km