Questions

Math Transition To College Math - Unit 2: Linear Systems

1) Define an algebraic equation and give an example.

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2) What is the replacement set or domain for a variable?

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3) Explain what a solution set is.

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4) Solve the equation.

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5) Solve the equation.

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6) Solve the equation.

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7) Solve the equation.

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8) Solve the equation.

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9) Solve for the indicated variable.

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10) Solve “A = 2ab + 2ac + 2bc” for “c”.

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11) Find a number such that 10 less than two-thirds the number is one-fourth the number.

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12) Find four consecutive even integers so that the sum of the first three is 2 more than twice the fourth.

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13) A rectangle 24 meters long has the same area as a square that is 12 meters on a side. What are the dimensions of the rectangle?

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14) Find the perimeter of a triangle and lengths of the sides if one side is 16 feet, another side is two-sevenths the perimeter, and the third side is one-third the perimeter.

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15) A chemical storeroom has a 90% acid solution and a 40% acid solution. How many centiliters of the 90% solution should be added to the 50 centiliters of the 40% solution to yield a 50% solution?

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16) How many gallons of hydrochloric acid must be added to 12 gallons of a 30% solution to obtain a 40% solution?

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Use substitution to solve the next four problems.

17) Solve.

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18) Solve.

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19) Solve.

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20) Solve.

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21) Explain how you solved the previous problem.

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Use elimination to solve the next four problems.

22) Solve.

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23) Solve.

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24) Solve.

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25) Solve.

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26) Explain how you solved the previous problem.

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Use systems of equations to solve the next four problems.

27) Steve had invested $12,000, part at 6% annual interest and the rest at 12% annual interest. If his total income from both investments is $1140 per year, how much is invested at 6%?

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28) Rachel wants to use cottage cheese and yogurt to increase the amount of protein and calcium in her daily diet. An ounce of cottage cheese contains 3 grams of protein and 12 milligrams of calcium. An ounce of yogurt contains 1 gram of protein and 44 milligrams of calcium. How many ounces of cottage cheese and yogurt should Rachel eat each day to provide 57 grams of protein and 840 milligrams of calcium?

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29) How many pounds of peanuts at $2.50 per pound and cashews at $3.60 per pound should be used to obtain 100 pounds of mixed nuts valued at $316.00?

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30) Becky is doing research in which she needs 28 grams of a substance that is 30% protein. How many grams of each two ingredients, one that is 50% protein and the other 25% protein, should she mix together?

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