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EQAO Grade 9 Math Applying Linear Systems to Situations — practice questions

Explore 6 free Applying Linear Systems to Situations questions in EQAO Grade 9 Math Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Applying Linear Systems to Situations questions and exercises with answers

Showing questions 1–6 of 6.

A small business works out the money coming in from sales of one product. Which rule gives that amount?Read the answer and worked solution →The costs rule for a business is built from two kinds of cost. Which pair does it hold?Read the answer and worked solution →For a business the costs rule is C(x) = 0.75x + 24000 and the sales rule is R(x) = 1.95x. What is the profit rule?Read the answer and worked solution →A costs rule is C(x) = 0.75x + 24000 and a sales rule is R(x) = 1.95x, both in dollars. How many units must be sold to break even?Read the answer and worked solution →One tank holds 60 litres and is gaining 8 litres a minute. Another holds 200 litres and is losing 6 litres a minute. After how long do the two hold the same volume?Read the answer and worked solution →Sort the money items by which sideRead the answer and worked solution →

Worked practice questions

A small business works out the money coming in from sales of one product. Which rule gives that amount?

  1. Amount sold added to the price of each
  2. Price of each divided by the amount sold
  3. Amount sold taken from the price of each
  4. Amount sold multiplied by the price of each
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Correct answer: D. Amount sold multiplied by the price of each

1. Money coming in from sales is worked out from how many were sold and what each one cost. 2. Selling 3 items at 5 dollars each brings in 15 dollars, which is 3 times 5. 3. So the amount is the quantity multiplied by the price, option D. 4. Adding or dividing the two would not even give an amount of money, so options A and B fail on units alone. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

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The costs rule for a business is built from two kinds of cost. Which pair does it hold?

  1. Only costs that change with the amount made
  2. Fixed costs such as rent plus running costs
  3. Only costs that stay the same every month
  4. Money taken in plus the wages that go out
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Correct answer: B. Fixed costs such as rent plus running costs

1. Some costs are the same whatever gets made, such as rent and wages, and these are the fixed costs. 2. Other costs rise and fall with the amount made, such as power and water, and these are the variable costs. 3. A costs rule adds the two kinds together, so both must appear. 4. Options A and C each keep only one of the two kinds. 5. Option D mixes money coming in with money going out, which belongs to two different rules. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

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For a business the costs rule is C(x) = 0.75x + 24000 and the sales rule is R(x) = 1.95x. What is the profit rule?

  1. P(x) = 2.7x - 24000
  2. P(x) = 1.2x + 24000
  3. P(x) = 1.2x - 24000
  4. P(x) = 0.6x - 24000
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Correct answer: C. P(x) = 1.2x - 24000

1. Profit is the money coming in with the costs taken away. 2. So write P(x) = 1.95x minus the whole of 0.75x + 24000. 3. The minus sign applies to both parts inside, giving 1.95x - 0.75x - 24000. 4. Subtracting the x terms gives 1.2x, so the profit rule is P(x) = 1.2x - 24000. 5. Option A adds the two x terms instead of subtracting them. 6. Option B keeps the 24000 positive, which would mean the fixed costs added to profit rather than eating into it. 7. Option D subtracts 0.75 twice over, which is a slip in the same subtraction. _Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_

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More Mathematics topics

Systems of Linear Equations in Two Variables