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| 1 | |
Before a commercial aircraft can take off, the pilot must ensure that the total mass does not exceed what is allowable. A standard mass of 86 kg is assumed for each male adult passenger and 70 kg for each female adult. A 20-seat aircraft fully loaded with male and female passengers has a total assumed passenger mass of 1528 kg. Let m represent the number of males, and f represent the number of females. Write a system of linear equations to model this situation.
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| | A) | Seats: m + f = 20 Mass: 86m + 70f = 1528 |
| | B) | Seats: m + f = 1528 Mass: 86m + 70f = 20 |
| | C) | Seats: m + f = 20 Mass: 70m + 86f = 1528 |
| | D) | Seats: m + f = 1528 Mass: 70m + 86f = 20 |
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| 2 | |
A local animal shelter has c cats and d dogs. A local animal lover has decided to donate a certain amount of money for each cat and dog in the shelter. The number of cats and dogs is modelled by the equation c + d = 55, and the total donation is modelled by the equation 10c + 5d = 475. Use the substitution method to determine the numbers of cats and dogs.
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| | A) | Cats: 15 Dogs: 40 |
| | B) | Cats: 30 Dogs: 25 |
| | C) | Cats: 40 Dogs: 15 |
| | D) | Cats: 25 Dogs: 30 |
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| 3 | |
A box containing three kittens of the same mass is on a scale. The scale reads 3.5 kg. Two more kittens, identical in mass to the first three, jump into the box. The reading on the scale increases to 4.5 kg. Model this situation with a linear system.
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| | A) | Let b represent the mass of the box and k represent the mass of each kitten.
3 kittens: b + 3k = 3.5 5 kittens: b + 5k = 4.5
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| | B) | Let k represent the mass of each kitten.
3 kittens: 3k = 3.5 5 kittens: 5k = 4.5
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| | C) | Let b represent the mass of the box and k represent the mass of each kitten.
3 kittens: b – 3k = 3.5 5 kittens: b – 5k = 4.5
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| | D) | Let b represent the mass of the box and k represent the mass of each kitten.
3 kittens: b + 3k = 4.5 5 kittens: b + 5k = 3.5
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| 4 | |
A local health food store sells peanut butter in bulk. The cost, in dollars, of each empty container is represented by c. The cost per kilogram of peanut butter is represented by p. One customer buys one container of peanut butter and the total cost is represented by c + 1.2p = 6.95. Another customer buys two containers of peanut butter and the total cost is represented by 2c + 2.5p = 14.45. Use the substitution method to determine the cost of each container and the cost of 1 kg of peanut butter.
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| | A) | Container: $5.50 Peanut Butter: $0.35 |
| | B) | Container: $0.35 Peanut Butter: $5.79 |
| | C) | Container: $0.35 Peanut Butter: $5.50 |
| | D) | Container: $1.00 Peanut Butter: $5.75 |
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| 5 | |
Consider the linear system 4x + 3y = 15 and 2x + y = 3. You plan to use the substitution method. What should you do first, and why? |
| | A) | Solve for x in the first equation. Always start with the first variable. |
| | B) | Solve for y in the second equation. The coefficient of y is 1. This makes solving for y easier, as well as making the substitution easier. |
| | C) | Solve for y in the first equation. The coefficient of 3 divides evenly into the constant 15. |
| | D) | It does not matter what you do first. All choices are of equal difficulty. |
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| 6 | |
| Basiruddin is solving a linear system using the substitution method. He has reached the line |  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0070002479/775989/Ch9_image003.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>]]> |
What should he do next?
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| | A) | Divide both sides by 3. |
| | B) | Divide both sides by 4. |
| | C) | Multiply both sides by 3. |
| | D) | Multiply both sides by 4. |
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| 7 | |
Consider the linear system 8x – 6y = 11 and –2x + 3y = 8. You plan to solve the system using the elimination method. Which is an appropriate first step in solving the system?
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| | A) | Multiply the second equation by 4 and add it to the first. |
| | B) | Multiply the second equation by 4 and subtract it from the first. |
| | C) | Multiply the second equation by 2 and subtract it from the first. |
| | D) | Add the two equations. |
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| 8 | |
Consider the linear system 2x – 3y = 12 and 5x + 2y = 11. Solve the system using the elimination method. |
| | A) | (–3, 2) |
| | B) | (3, –2) |
| | C) | (3, 2) |
| | D) | (2, –3) |
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| 9 | |
In a hardware store, steel chain sells for $1.50/ft, while brass chain sells for $4.20/ft. Sabariah bought a total of 25 ft of chain and paid $83.40. Model this situation using a linear system.
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| | A) | Let s represent the length of the steel chain and b represent the length of the brass chain.
Length of chain: s + b = 83.4 Cost: 1.5s + 4.2b = 25
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| | B) | Let s represent the length of the steel chain and b represent the length of the brass chain.
Length of chain: s + b = 83.4 Cost: 4.2s + 1.5b = 25
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| | C) | Let s represent the length of the steel chain and b represent the length of the brass chain.
Length of chain: s + 4.2b = 25 Cost: 1.5s + b = 83.4
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| | D) | Let s represent the length of the steel chain and b represent the length of the brass chain.
Length of chain: s + b = 25 Cost: 1.5s + 4.2b = 83.4
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| 10 | |
A customer purchased m bags of sheep manure and t bags of topsoil. The total number of bags is modelled by the equation m + t = 35 and the total cost is modelled by the equation 9.50m + 7.50t = 296.50. Determine the number of bags of each gardening product. Use the elimination method.
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| | A) | Sheep manure: 17 bags Topsoil: 18 bags |
| | B) | Sheep manure: 18 bags Topsoil: 17 bags |
| | C) | Sheep manure: 20 bags Topsoil: 15 bags |
| | D) | Sheep manure: 15 bags Topsoil: 20 bags |
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