Download word SYSTEMNS C

EVENT:
NAME________________________
SET UP THE EQUATIONS THAT CAN BE USED TO SOLVE THE PROBLEMS. IDENTIFY YOUR VARIABLES
CAREFULLY!!! YOU DO NOT HAVE TO SOLVE THEM. THEY MAY NOT BE SOLVABLE!!
1. Jenny has 24 coins consisting of nickels and quarters. The total value of the coins is $3.00. How many coins of each kind
does Jenny have?
2. Jared’s boat traveling downstream can go 15 miles in 2 hours. The same boat traveling upstream can only make 2/3 of this
distance in twice the amount of times. What is the rate of the boat in still water? What is the rate of the current?
3. When the digits of a two-digit number are reversed, the resulting number is 54 less than the original number. The tens digit of
the original number is 4 times the units digit. What is the original number?
4. If one is added to the numerator and the denominator of a fraction, the result equals 1/2. If one is subtracted from the
numerator and denominator of the same fraction, the result equals 1/3. What is the original fraction?
5. Five years ago, Larry was 4 times as old as Jen. Six years from now, Larry will be 9 years more than twice Jen’s age. How
old is each now?
6. An investor purchased two kinds of securities, one paying 2% and the other paying 4%, and got an annual income of $900. If
he had reversed the amounts invested, his income would have been only $600. How much did he invest at each rate?
7. Find a number of three-digits if the units’ digit is 1/2 the tens’ digit, the hundreds’ digit is three times the tens’ digit, and the
number is 27 more than 77 times the sum of the digits.
8.
Find three positive numbers in increasing order such that the difference of the first two numbers is two, the difference of
the first and last numbers is 4, and the quotient of the last two numbers is 1.2.
9. In a math contest, each team is asked 50 questions. The teams get 15 points for each correct answer and lose 8 points for each
incorrect answer. Our team finished with a score of 566. How many questions did our team answer correctly?
10.
The girls in our class bought chocolate kisses worth $2.79 per ounce. The boys bought M&M’s worth $1.23 per ounce. They
combine the two and sell 40 ounces for $1.61 per ounce. How many ounces of M&M’s did the boys buy?
II. Find the minimum and maximum values of the objective function subject to the given constraints. Sketch the graph. Show all
work.
Objective function :
C  5x  2y
Constraint s :
x 0
y 0
2x  y  8
x  3y  9
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EXTRA CREDIT Solve the problems for full credit.
1.A bakery is making whole-wheat bread and apple bran muffins. For each batch of bread they make $35 profit. For each batch of
muffins they make $10 profit. The bread takes 4 hours to prepare and 1 hour to bake. The muffins take 1/2 hour to prepare and 1/2
hour to bake. The maximum preparation time available is 16 hours. The maximum baking time available is 10 hours. How many
batches of bread and muffins should be made to maximize profits?
a.
b.
c.
What are the constraints?
What is the objective function?
How many muffins and bread must be made for a maximum profit? What is the profit?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
2. Find a two-decimal-place number between zero and one such that the sum of its digits is 9 and if the digits are reversed, the number
is increased by 0.27.
3. Joe Slippery Fingers robs a bank in Gulchville. His loot is $10,000 in paper money. He makes his getaway at noon in a plane flying
toward the border at 600 mph. A few minutes later, Sam Ketchem, the local policeman, takes off after Joe in a plane flying 800 mph.
The border is 1,000 miles away. The bag with the money is open and lies near a crack in the floor of the plane. The wind pressure
outside pulls the bills out of the crack at the rate of $100 per minute. If Sam catches up to Joe and forces him down just at the border,
how much of the loot was recovered?