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# 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?