[discia] GCSE Maths › Algebra › Forming and Solving Equations

Forming and Solving Equations

discia.org 10 questions · 38 marks
Name Date
  1. Either paper 4 marks

    Amara and Ben share 112 counters between them.

    Ben gets 22 more counters than Amara.

    Amara gets \(x\) counters.

    (a)

    Write down an equation in terms of \(x\).

    (b)

    Solve your equation to find the value of \(x\).

    (c)

    Write down how many counters Ben gets.

    Show answer
    (a) \(2x + 22 = 112\)
    (b) \(45\)
    (c) \(67\)
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  2. Either paper 3 marks

    Four positive whole numbers add up to 84.

    One of the numbers is a multiple of 20.

    The other three numbers are equal.

    What are the four numbers?

    Show answer
    \(8, 8, 8\) and \(60\)
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  3. Either paper 3 marks

    Multiplying \(y\) by 5 gives the same result as adding 20 to \(y\).

    (a)

    Write this as an equation.

    (b)

    Show that the value of \(y\) is not 4.

    Show answer
    (a) \(5y = y + 20\)
    (b) When \(y = 4\), the left side is \(20\) and the right side is \(24\). These are not equal, so \(y\) is not 4.
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  4. Either paper 3 marks

    The sum of three consecutive odd numbers is 51.

    Work out the three numbers.

    Show answer
    \(15\), \(17\) and \(19\)
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  5. Either paper 4 marks

    The three sides of a triangle have lengths \(2x + 9\) cm, \(3x - 2\) cm and \(x + 3\) cm.

    The perimeter of the triangle is 40 cm.

    (a)

    Find the value of \(x\).

    (b)

    Write down the length of the longest side of the triangle.

    Show answer
    (a) \(5\)
    (b) \(19\ \text{cm}\)
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  6. Either paper 2 marks

    \(2a + 2b = 9\) and \(16x + 16y = 136\)

    Show that \(8a + 8b\) has a greater value than \(4x + 4y\).

    Show answer
    \(8a + 8b = 36\) and \(4x + 4y = 34\), so \(36 > 34\)
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  7. Either paper 6 marks

    Marcus buys 4 metres of linen at £13.10 per metre.

    He also buys 6 metres of cotton.

    The total cost is £112.40.

    (a)

    Work out the cost of one metre of cotton.

    (b)

    Buttons cost 53p each.

    The greatest number of buttons Marcus can buy with £9 is 16.

    Marcus says, "The greatest number of buttons I can buy with £18 is 32 because £18 is double £9."

    Is Marcus correct?

    You must show your working.

    Show answer
    (a) \(£10.00\)
    (b) No: with £18 Marcus can buy 33 buttons, and \(2 \times 16 = 32\), which is not equal to 33
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  8. Either paper 4 marks

    Kofi is twice as old as Ella.

    In 8 years' time the sum of their two ages will be 61.

    Work out how old Ella is now.

    Show answer
    \(15\ \text{years}\)
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  9. Either paper 4 marks

    £195 is shared between Maya, Nico and Orla.

    Nico gets three times as much as Maya.

    Orla gets £10 more than Maya.

    Work out how much Nico gets.

    Show answer
    \(\text{£}111\)
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  10. Either paper 5 marks

    Beacon and Kingsway are two swimming clubs.

    Beacon charges a joining fee of £60 and then £21 for each month of membership.

    Kingsway charges a joining fee of £108 and then £17 for each month of membership.

    (a)

    Calculate the number of months for which the total cost at Beacon is the same as the total cost at Kingsway.

    (b)

    Work out that total cost.

    Show answer
    (a) \(12\ \text{months}\)
    (b) \(\text{£}312\)
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discia.org Forming and Solving Equations · sheet 1
Answers Forming and Solving Equations · sheet 1
  1. (a) \(2x + 22 = 112\)
    (b) \(45\)
    (c) \(67\)
  2. \(8, 8, 8\) and \(60\)
  3. (a) \(5y = y + 20\)
    (b) When \(y = 4\), the left side is \(20\) and the right side is \(24\). These are not equal, so \(y\) is not 4.
  4. \(15\), \(17\) and \(19\)
  5. (a) \(5\)
    (b) \(19\ \text{cm}\)
  6. \(8a + 8b = 36\) and \(4x + 4y = 34\), so \(36 > 34\)
  7. (a) \(£10.00\)
    (b) No: with £18 Marcus can buy 33 buttons, and \(2 \times 16 = 32\), which is not equal to 33
  8. \(15\ \text{years}\)
  9. \(\text{£}111\)
  10. (a) \(12\ \text{months}\)
    (b) \(\text{£}312\)
discia.org Forming and Solving Equations · sheet 1