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Directions: You will need paper and pencil. Prepare a solution using simultaneous equations (a system of equations). Be sure to show all of your work. The solutions presented will show one solution method. Other methods are also possible.
1. |
A pharmacy sells two peroxide solutions. Solution A contains 2% peroxide, and solution B contains 7% peroxide. The pharmacy mixes these two solutions to create 50 milliliters of a third solution, solution C, containing 4% peroxide.
The system below represents this situation:
x + y = 50
0.02x + 0.07y = (0.04)(50) |
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a) What does x represent?
b) When graphed, what is the x-coordinate of the intersection of the two lines?
c) How many milliliters of solution B will be needed to mix with solution A to create solution C? |
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2. |
Alan buys several cases of a discontinued shampoo which he is selling at a reduced price. The amount of revenue, in y dollars, that he receives from selling x bottles of shampoo is represented by y = 5x. Alan's cost of selling x bottles of the shampoo is represented by
y = ¼ x + 114.
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a) How many bottles of shampoo must Alan sell before his cost and the revenue are equal?
b) What does 114 represent?
c) Using your answer from part a, explain what the graph of this situation is telling you?
d) Is there a maximum value that will be reached by x? Explain. |
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3. |
Drucila is responsible for buying a week's supply of food and medication for the dogs and cats at a rescue shelter. She needs to feed 164 cats and 24 dogs. The food and medication for each dog costs twice as much as those supplies for a cat. Her budget is $4240.
a) How much can Drucila spend in a week on each cat for food and medication?
b) How much can Drucila spend in a week on each dog for food and medication?
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4. |
Mr. Allen is planning a twenty question quiz worth 100 points. The quiz will contain True/False questions worth 3 points each and multiple choice questions worth 11 points each.
a) How many multiple choice questions will be on the quiz?
b) How many True/False questions will be on the quiz?
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5. |
While planning a backpacking trip, Gwen and Ari, check out two water containers (canteens). They know that one of the larger containers and two of the smaller containers yields a total of 8 cups of water. They also know that one large container minus one small container yields 2 cups of water.
a) How many cups of water can be held by the smaller container?
b) How many cups of water can be held by the larger container?
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6. |
A dirt bike trail extends between Jonesville and Smithville which are 30 miles apart. Larry and Chuck plan a marathon dirt bike race between the two villages. Since Chuck is younger, Larry gives him a 10 mile head start. Chuck travels at 10 mph and Larry travels at 20 mph. Assume a constant speed along the trail. |
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a) Write linear equations to represent each boy during the race.
b) Prepare a graph representing the race.
c) At what time will Larry catch up with Chuck?
d) How far will they have traveled when they meet?
e) Who will win the race? Explain.
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7. |
A company manufactures widgets at $25 each and others at $50 each. The company sold 60 widgets and collected $2025.
a) Find the number of $25 widgets sold.
b) Find the number $50 widgets sold.
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