System of Linear Equation Word Problems:
1. At a dance party, a group of boys and girls exchange dances as follows: one boy dances with 5 girls, a second boy second with 6 girls, and so on, the last boy dancing with all the girls. If b represents the number of boys and g the number of girls, then find b in terms of g.
2. George Washington was born 11 years before Thomas Jefferson. In 1770, Washington's age was 3 more than 7 times the age of Jefferson in 1748. What was the sum of the two men's ages in 1750.
3. Four pounds of onions costs the same as 2 pounds of string beans. At the same time, 1 pound of string beans costs 3 times as much as a pound of potatoes, while 1 pound of onions costs 4 cents less than 2 pounds of potatoes. What is the total cost of 1 pound of each of the vegetables?
4. Find two consecutive odd integers such that 1/3 the smaller plus twice the larger equals 7 more than the sum of the two numbers.
5. In a basketball game, the U.S. has 4 times as many points as Croatia. A Croatian makes a basket for 3 points, at which point the United States only has 3 times as many points. How many points does the U.S. have?
6. Mike and Joey bought identical loaves of bread and packages of bologna. Mike made sandwiches with 5 slices of bologna and had 4 slices of bread left when he ran out of meat. Joey made sandwiches with 4 slices of bologna and had 4 slices of meat when he ran out of bread. Each boy only started with one loaf and each sandwich has two slices of bread. How many slices of bread were in each loaf?
7. Sue has $3.08 in pennies, nickels, and quarters. She has 4 more pennies than quarters and one more nickel than pennies. How many nickels does she have?
8. K takes 30 minutes less time than M to travel a distance of 30 miles. K travels 1/3 mile per hour faster than M. If x is K's rate of speed in miles per hour, then find K's time for the distance in terms of x.
9. What is the value of x if 1 minus the reciprocal of (1–x) equals the reciprocal of (1–x)?
10. A train traveling from Aytown to Beetown meets with an accident after 2 hour. The train is stopped for 30 minutes, after which it proceeds at four-fifths of its usual rate, arriving at Beetown 2 hours late. If the train had covered 80 miles more before the accident, it would have been just one our late. What is the usual rate of the train?
11. Adam can do a job in 10 days, while Brenda takes 15 days to do it. After Brenda works 3 days, Adam and Brenda work together to finish the job. How many days did Adam work?
12.A car travels 120 miles from A to B at 30 miles per hour but returns the same distance at 40 miles per hour . What is the average speed for the round trip?
13. One car left a city at 2:00 pm and traveled at an average speed of 40 miles per hour. A second car left at 4:00 pm, traveled the same route, and overtook the first car at 9:00 pm. What was the average speed in miles per hour of the second car?
14. A man can do a job in 9 days and his son can do the same job in 16 days. They start working together. After 4 days, the son leaves and the father finishes the job alone. How many days does the man take to finish the job?
15. Twenty-five women did 1/5 of a job in 8 days. Then, because of an emergency, it became necessary to complete the job in the next 20 days. How many additional women needed to be added to the crew of 25 to accomplish this?
16. Two bicyclists are seven-eighths of the way through a mile-long tunnel when a train approaches the closer end at the 40 mph. The riders take off at the same speed in opposite directions, and each escapes the tunnel as the train passes them. How fast did they ride?
17. A train, x meters long, traveling at a constant speed, takes 20 seconds from the time it first enters a tunnel 300 meters long until the time it completely emerges from the tunnel. One of the stationary ceiling lights in the tunnel is directly above the train for ten seconds. Find x.
18. Two men starting at a point on a circular 1-mile race track walk in opposite with uniform speeds and meet in 6 minutes, but if they walk in the same direction, it requires one hour for the faster walker to gain a lap. What is the rate of the slower walker?
19. A crew of 30 people can build a certain road in 60 days. After the tenth day the plans are changed; the company wants the road built in 30, not 60, days. How many more people must be hired?
20. Jack and Jill went up the hill at a rate of 8 units per minute. They came tumbling down at a rate of 8 units per second. What was their average rate, in units per minute, for the round trip?
21. Two dogs, each traveling 10 ft/sec, run toward each other from 500 feet apart. As they run, a flea flies from the nose of one dog to the nose of the other at 25 ft/sec. The flea flies between the dogs in this manner until it is crushed when the dogs collide. How far did the flea fly?
22. Find the ordered pair (x, y) that is the solution of the system:
x + 2y = 11
xy 12
2x – 2y = 2
xy 3
23. Find the value of x/y if (3/√y) — (1/√x) = 2/(√x + √y)
24. When three numbers are added tow at a time, the sums are 29, 46, and 53. What is the sum of all three numbers?
25. Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour. With only valves A and C open, it takes 1.5 hours. With only valves B and C open, it takes 2 hours. How long will it take to fill the tank with only valves A and B open?
