Printable · GCSE Foundation · ages 14-16

Forming and solving equations from situations worksheet — GCSE Foundation

Fifteen questions on "forming and solving equations from situations" — DfE statement A21. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Forming and solving equations from situations worksheet — GCSE Foundation

Maths · GCSE Foundation · A21 · Forming and solving equations from situations · 15 questions

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1.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.
(a)6c
(b)6 + c
(c)c ÷ 6
(d)c − 6
2.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.
(a)2 + 3m
(b)3 + 2m
(c)5 + m
(d)5m
3.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30
4.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.
(a)3x
(b)x − 3
(c)x/3
(d)x + 3
5.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.
(a)£2.48
(b)£3.30
(c)£2.80
(d)£3.80
6.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.
(a)b − 15
(b)b + 15
(c)b/15
(d)15b
7.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.
(a)x + 3
(b)3 − x
(c)x − 3
(d)3x
8.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.
(a)9.5
(b)8
(c)17.5
(d)4.75
9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.
(a)No — it has never happened and never will
(b)Yes — when Harry is 20
(c)No — that moment has already passed
(d)Yes — when Harry is 16
10.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
(a)12
(b)8
(c)36
(d)6
11.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.
(a)24
(b)18
(c)15
(d)12
12.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.
(a)7.4
(b)1.25
(c)5
(d)4
13.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.
(a)Subtracting 4x gives 3 = 10, which is never true.
(b)x would have to be negative, but x must be positive.
(c)It's true for every x, so there are infinite solutions.
(d)x = 7, since 10 − 3 = 7.
14.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.
(a)25
(b)24
(c)21
(d)23
15.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.
(a)12
(b)6
(c)7.5
(d)9

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