linear Equations

1. The sum of two numbers is 66. The larger number is three less than twice the
smaller number. Find the numbers.

2. A supermarket had a one day sale on Pepperidge Farm cookies. It sold three
times as many packages of chocolate-chip cookies as oatmeal, and twice as many
fudge-almond as oatmeal. If the supermarket sold 600 packages in one day, how
many packages of each did it sell?

3. Otis lives one mile away from Tina. They begin to bicycle toward each other at
the same time. The road from Otis’s house to Tina’s is downhill; so Otis can travel
twice as fast as Tina, who peddles her bike uphill at 4 miles/hour. For the entire
time of Otis’ and Tina’s journey, a fly travels back and forth between them at 12
miles/hour. How far will the fly fly?

4. In an FBI sting operation a group of agents leave a warehouse at 234 Vassar
Street and move at 4 miles/hour to a second warehouse at 432 Rassav Street, eight
miles from the Vassar Street warehouse. At the same time several members of the
mob also move from the Vassar Street warehouse to the Rassav Street warehouse;
but they move at a slower speed of 3 miles/hour. How much time will the FBI
have at the Rassav Street warehouse before the mob arrives?

5. A compulsive gambler doubles his money at roulette. Feeling lucky he decides
to play blackjack and loses $400. He returns to the roulette table and, once again,
doubles his money. He seems to always lose when he plays blackjack and always
win when he plays roulette. No matter, he decides to push his luck and play crap
once more, only to lose another $400. If he ends with $20.00, how much money
did he start with?

6. Two different kinds of tea are to be mixed to produce 3 pounds of tea that is
valued at $3.20 /pound. If the value of the first and second kinds of tea are $3.80
and $2.70, respectively, how many pounds of tea of each type should go into the
mixture?

7. A hobo was one fourth across a railroad bridge when he heard the train coming
from behind. There was not enough room on the bridge for a person and a train.
If the train was exactly one bridge-length away, which way should he run and
why?

8. John Quizwiz averaged 73%, 84%, 68%, 89% and 91% on the first 5 Workouts
of this worktext, respectively. If he averaged 100% on Workouts 6, 7, 8 and 9,
what should he average on this Workout, in order that his average over the first
10Workouts be 90%?

9. A nursery mixes three different kinds of grass seed–clover, alfalfa and bluegrass.
The clover sells for $0.42 per pound; but the nursery has only 20 pounds
left, and must use it all. The alfalfa sells for $0.35 per pound and the bluegrass
for $0.55 per pound; but there are ample supplies of alfalfa and bluegrass. How
much of each should be in the mixture, if the nursery can mix 100 pounds to be
sold at $0.45 per pound?

10. Professor Egghead can write an algebra textbook in 18 months. Professor
Wizzard can write one in one year. How long would it take them if they worked
together?

11. Le Capital, is the French National Railroad’s high speed train that links Paris
to Marseille. It travels at an average speed of 210 kilometers/hour when traveling
from Paris to Marseille and 190 kilometers/hour on returning from Marseille to
Paris. What is the average speed of the train in making the journey back and
forth?

12. A jumbo jet is on route from Boston to San Francisco. During the first half of
the trip it averages 580 miles/hour. During the second half, the pilot decides to
increase the average speed by 20 miles/hour. What will the final average speed
be?

13. It is 9:00 a.m. (Pacific Time) in San Francisco when it is 12:00 p.m. (EST) in
Boston. In Problem 12, assume that the plane left Boston at 12:00 p.m. (EST) and is
scheduled to arrive at 1:50 p.m. ; and assume, once again, that the plane traveled
half the 3000 distance between Boston and San Francisco at an average speed of
580 miles per hour. If the pilot decided to increase the average velocity during the
second half of the trip in order to arrive at San Francisco on time, what should the
average velocity of the plane be for the second half of the trip?