Forming and solving Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Forming and solving questions. See exactly how to solve problems on forming an equation, solving one-step equations, inverse operations, money context.

forming an equationsolving one-step equationsinverse operationsmoney contextinterpreting the solutionperimeter
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
I think of a number and add 77. The answer is 1212. Using nn for the number, form an equation and solve it to find the number.

Worked solution

  1. Form the equation

    n+7=12n + 7 = 12

    The number is nn, and adding 77 to it gives 1212.

  2. Solve the equation

    n=12−7=5n = 12 - 7 = 5

    Subtract 77 from both sides to undo the addition.

  3. Interpret the answer

    n=5n = 5

    The number I thought of is 55. Check: 5+7=125 + 7 = 12.

Answer
n=5n = 5
Question 2
1 markeasy
I think of a number and multiply it by 44. The answer is 2020. Using nn for the number, form an equation and solve it.

Worked solution

  1. Form the equation

    4n=204n = 20

    Multiplying the unknown number nn by 44 gives 2020.

  2. Solve the equation

    n=204=5n = \frac{20}{4} = 5

    Divide both sides by 44 to undo the multiplication.

  3. Interpret the answer

    n=5n = 5

    The number I thought of is 55. Check: 4×5=204 \times 5 = 20.

Answer
n=5n = 5
Question 3
1 markeasy
I think of a number and subtract 33. The answer is 99. Form an equation using nn and solve it to find the number.

Worked solution

  1. Form the equation

    n−3=9n - 3 = 9

    Taking 33 away from the number nn leaves 99.

  2. Solve the equation

    n=9+3=12n = 9 + 3 = 12

    Add 33 to both sides — addition undoes subtraction.

  3. Interpret the answer

    n=12n = 12

    The number I thought of is 1212. Check: 12−3=912 - 3 = 9.

Answer
n=12n = 12
Question 4
2 markseasy
Five identical books cost £37.50 in total. Let bb be the cost of one book in pounds. Form an equation and solve it to find the cost of one book.

Worked solution

  1. Form the equation

    5b=37.505b = 37.50

    Five books each costing £b\pounds b come to £37.50\pounds 37.50.

  2. Solve the equation

    b=37.505=7.50b = \frac{37.50}{5} = 7.50

    Divide both sides by 55.

  3. Interpret the answer in context

    b=7.50⇒£7.50b = 7.50 \Rightarrow \pounds 7.50

    The value of bb is a price, so one book costs £7.50\pounds 7.50 — money is written to 22 decimal places.

Answer
£7.50\pounds 7.50
Question 5
2 markseasy
A rectangle has length xx cm and width 44 cm. Its perimeter is 2626 cm. Form an equation and solve it to find xx.

Worked solution

  1. Form the equation

    2(x+4)=262(x + 4) = 26

    The perimeter of a rectangle is 2×(length+width)2 \times (\text{length} + \text{width}).

  2. Solve the equation

    x+4=13⇒x=9x + 4 = 13 \Rightarrow x = 9

    Divide both sides by 22, then subtract 44.

  3. Interpret the answer in context

    x=9 cmx = 9 \text{ cm}

    The length is 99 cm. Check: 2(9+4)=262(9 + 4) = 26 cm, and a length of 99 cm is positive, so it is sensible.

Answer
x=9 cmx = 9 \text{ cm}

Unlock 65 more Forming and solving questions

Create a free account to work through every GCSE Forming and solving question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Forming and solving practice

Hard QuestionsPractice Questions

Related Algebra topics

Algebraic fractionsEquation of a circleCoordinatesCubic and reciprocal graphsExponential and trig graphsExpanding binomials