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Math 8

Math 8 · Worksheets

Mixed review · Percents, ratios and equations

Ten questions of mixed difficulty, covering Equations and graphs, Percents, ratios and rates. Print it, or work through it on screen — the answer key starts on its own page.

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Mixed review · Percents, ratios and equations

Math 8 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. A 500 g bag of trail mix costs $3.50 and a 750 g bag costs $4.80. Which is the better buy, and why?

    1. a) The 500 g bag: it costs $1.30 less than the 750 g bag.
    2. b) The 500 g bag: it gives 143 g per dollar, against 156 g.
    3. c) The 750 g bag: bigger packages always cost less per gram.
    4. d) The 750 g bag: it costs 64¢ per 100 g, against 70¢.

  2. Solve −2(x − 5) = 18.

    1. a) x = 4
    2. b) x = 14
    3. c) x = −4
    4. d) x = −14

  3. On a map, 2 cm stands for 15 km. Two towns are 7 cm apart on the map. How far apart are they really?

    1. a) 20 km
    2. b) 105 km
    3. c) 52.5 km
    4. d) 30 km

  4. A taxi charges $4 plus $2 for each kilometre. Which points belong in its table of values, with distance in km first and cost in dollars second?

    1. a) (0, 4), (1, 6), (2, 8)
    2. b) (4, 0), (6, 1), (8, 2)
    3. c) (0, 0), (1, 6), (2, 12)
    4. d) (0, 2), (1, 6), (2, 10)

  5. A candle is 30 cm tall and burns down 2 cm every hour. Its table of values starts (0, 30), (1, 28), (2, 26), (3, 24). After how many hours will it be 10 cm tall?

    1. a) 5 hours
    2. b) 10 hours
    3. c) 20 hours
    4. d) 15 hours

  6. Which of these is a rate?

    1. a) 90 km in 1.5 hours
    2. b) 2 wins for every 3 losses
    3. c) 3 red cars to 5 blue cars
    4. d) 4 cups of flour to 1 cup of sugar

  7. Solve x/3 = −5.

    1. a) x = −8
    2. b) x = −2
    3. c) x = −15
    4. d) x = 15

  8. Ana cycles 18 km in 45 minutes. At that rate, how far does she cycle in 2 hours?

    1. a) 48 km
    2. b) 0.8 km
    3. c) 36 km
    4. d) 80 km

  9. Solve −6x = 42.

    1. a) x = 7
    2. b) x = −252
    3. c) x = 48
    4. d) x = −7

  10. Solve 3(x + 4) = 27.

    1. a) x = 23
    2. b) x = 5
    3. c) x = 13
    4. d) x = 9

Answer key · Mixed review · Percents, ratios and equations

Math 8 · maddyhelps.com

  1. d) The 750 g bag: it costs 64¢ per 100 g, against 70¢. — Compare the price of the same amount: $3.50 ÷ 5 = 70¢ per 100 g and $4.80 ÷ 7.5 = 64¢ per 100 g, so the 750 g bag is cheaper for each gram. A lower total price just means a smaller bag, and with grams per dollar, more is better — 156 g beats 143 g. Big packages are often cheaper per gram, but not always, which is why you check.
  2. c) x = −4 — Divide both sides by −2, x − 5 = −9, then add 5: x = −4. Check: −2 × (−4 − 5) = −2 × (−9) = 18 ✓. x = 14 divides 18 by 2 instead of −2, and x = −14 multiplies out as −2x − 10, forgetting that −2 × (−5) = +10.
  3. c) 52.5 km — 1 cm stands for 15 ÷ 2 = 7.5 km, so 7 cm stands for 7 × 7.5 = 52.5 km. 105 km multiplies 7 by 15, as if each centimetre stood for 15 km, and 20 km adds 5 to both numbers because 7 is 5 more than 2 — but a scale multiplies, it does not add.
  4. a) (0, 4), (1, 6), (2, 8) — At 0 km the cost is just the $4 charge, and each kilometre adds $2: (0, 4), (1, 6), (2, 8). (0, 2), (1, 6), (2, 10) swaps the $4 and the $2, and (4, 0), (6, 1), (8, 2) has the right numbers with the coordinates the wrong way round.
  5. b) 10 hours — The candle has to lose 30 − 10 = 20 cm at 2 cm an hour, which takes 20 ÷ 2 = 10 hours — extend the table and you reach (10, 10). 15 hours is when it burns down completely, and 20 hours counts the centimetres it loses as if they were hours.
  6. a) 90 km in 1.5 hours — A rate compares two quantities measured in different units — here kilometres and hours — so it can be written as a unit rate, 60 km/h. The others compare things counted or measured in the same unit, cars to cars or cups to cups, which makes them ratios.
  7. c) x = −15 — x divided by 3 gives −5, so multiply both sides by 3: x = −15. Check: −15 ÷ 3 = −5 ✓. x = 15 loses the sign, and −8 subtracts 3 instead of multiplying — a division is undone by multiplying.
  8. a) 48 km — 45 minutes is ¾ of an hour, so her rate is 18 ÷ ¾ = 24 km/h, and in 2 hours she goes 48 km. 80 km writes 45 minutes as 0.45 h — but an hour has 60 minutes, not 100 — and 36 km treats 45 minutes as a whole hour.
  9. d) x = −7 — Divide both sides by −6: x = 42 ÷ (−6) = −7. Check: −6 × (−7) = 42 ✓. x = 7 forgets that a positive divided by a negative is negative, and its check fails: −6 × 7 = −42.
  10. b) x = 5 — Divide both sides by 3 first, x + 4 = 9, then subtract 4: x = 5. Check: 3(5 + 4) = 3 × 9 = 27 ✓. x = 9 stops halfway — 9 is x + 4, not x — and x = 13 adds the 4 instead of subtracting it.