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Exam 4: Linear Systems

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Sobeys sells fruit trays consisting of pineapple and melons. The manager of the fruit department obtains pineapples at a wholesale price of $2.50 per kg, grapes at $2.15 per kg, strawberries at $1.50 per kg and melons at $1.85 per kg. He is required to produce 10 kg of the mixed fruit. He is required to add 2 kg of strawberries and 3 kg of grapes. What is the maximum weight of pineapple that he can put in the mix in order to have an effective wholesale cost no greater than $2.00 per kg?

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Cost of 2 kg of strawberries = $1.50 × 2 = $3.00
Cost of 3 kg of grapes = $2.15 × 3 = $6.45
Total cost of the mixed fruit = $2 × 10 = $20
Cost of pineapple and melons = $20 - ($3 + $6.45) = $10.55 ⇒ 2.5p + 1.85m = 10.55
Maximum weight of pineapple and melons = 10 - (2 + 3) = 5kg ⇒ p + m = 5
2.5p + 1.85m = 10.55 Cost of 2 kg of strawberries = $1.50 × 2 = $3.00 Cost of 3 kg of grapes = $2.15 × 3 = $6.45 Total cost of the mixed fruit = $2 × 10 = $20 Cost of pineapple and melons = $20 - ($3 + $6.45) = $10.55 ⇒ 2.5p + 1.85m = 10.55 Maximum weight of pineapple and melons = 10 - (2 + 3) = 5kg ⇒ p + m = 5 2.5p + 1.85m = 10.55 0.65p = 10.55 - 9.25 = 2 0.65p = 10.55 - 9.25
Cost of 2 kg of strawberries = $1.50 × 2 = $3.00 Cost of 3 kg of grapes = $2.15 × 3 = $6.45 Total cost of the mixed fruit = $2 × 10 = $20 Cost of pineapple and melons = $20 - ($3 + $6.45) = $10.55 ⇒ 2.5p + 1.85m = 10.55 Maximum weight of pineapple and melons = 10 - (2 + 3) = 5kg ⇒ p + m = 5 2.5p + 1.85m = 10.55 0.65p = 10.55 - 9.25 = 2 Cost of 2 kg of strawberries = $1.50 × 2 = $3.00 Cost of 3 kg of grapes = $2.15 × 3 = $6.45 Total cost of the mixed fruit = $2 × 10 = $20 Cost of pineapple and melons = $20 - ($3 + $6.45) = $10.55 ⇒ 2.5p + 1.85m = 10.55 Maximum weight of pineapple and melons = 10 - (2 + 3) = 5kg ⇒ p + m = 5 2.5p + 1.85m = 10.55 0.65p = 10.55 - 9.25 = 2 = 2
Cost of 2 kg of strawberries = $1.50 × 2 = $3.00 Cost of 3 kg of grapes = $2.15 × 3 = $6.45 Total cost of the mixed fruit = $2 × 10 = $20 Cost of pineapple and melons = $20 - ($3 + $6.45) = $10.55 ⇒ 2.5p + 1.85m = 10.55 Maximum weight of pineapple and melons = 10 - (2 + 3) = 5kg ⇒ p + m = 5 2.5p + 1.85m = 10.55 0.65p = 10.55 - 9.25 = 2

Graph: y = -6

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Graph: y > -2x

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The entirety of the plane to the right of the line is the answer. The entirety of the plane to the right of the line is the answer.

Solve the system of equations: 3x + y = 13 x - 6y = 7

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Question 4

Solve graphically: y = -x - 5 and x - y = 6

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Question 5

Bonny and Clyde divide a profit of $15 700. If Clyde is to receive $4200 more than one-fifths of Bonny's share, how much will Bonny receive?

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Question 6

Solve graphically: 5x - 2y = 10 and y = 5

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Question 7

Find the slope of the line: 4y = 5(y + 3)

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Question 8

A bakery has been baking 4000 donuts a day for distribution. . The second shift has produced 1000 donuts fewer than two-thirds of the number of donuts produced by the first shift. Determine the number of donuts each shift has produced.

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Question 9

How many solutions does the following system of linear equations have? x = 3y + 4 3x - 9y = 13

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Question 10

The difference between seven times the first number and three times the second number is 12. The sum of three-fourths of the first number and two-thirds of the second number is 21. Find the two numbers.

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Question 11

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

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Question 12

It takes a snowboarder 46 minutes to descend from an elevation of 9200 metres to an elevation of 4508 metres. What is the rate of descent (slope) per minute?

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Question 13

Find the slope and y-intercept: -6y - 24 = 5x

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Question 14

Graph: x = -4

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Question 15

Graph: x + 4y = 8

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Question 16

Solve graphically: 2x + 3y = -4 and x - 2y = 5

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Question 17

A couple is about the get married. They decide to start a joint bank account to save for a house. They want to have an initial investment of $9000. The first partner contributes $350 more than three-quarters what the second partner contributes. How much does each partner contribute?

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Question 18

It takes a car 10 seconds to increase its speed from from 60 k/hr to 90 k/hr. What is the rate of acceleration (slope) in k/hr/sec?

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Question 19

A machine requires five hours to make a unit of Product A and four hours to make a unit of Product B. Last month the machine operated for 440 hours producing a total of 100 units. How many units of each type of product did it produce?

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