Forming equations and formulae from words

The angles of a triangle are (x + 10)°, 2x° and (3x − 10)°.

Work out the size of the largest angle of the triangle.

Dan and Ella share 45 sweets.

Ella gets 7 more sweets than Dan.

Dan says, "I got 20 sweets."

Is Dan right? You must show how you get your answer.

A pen costs c pence.

1. Write an expression for the cost, in pence, of 8 pens.
2. A ruler costs 35p. Write an expression for the total cost, in pence, of 8 pens and 1 ruler.

A trapezium has parallel sides of length (2x + 1) cm and (4x + 3) cm.

The perpendicular height of the trapezium is 6 cm.

Show that the area of the trapezium is 6(3x + 2) cm².

A rectangle has length (3x + 2) cm and width (x − 1) cm.

The perimeter of the rectangle is 50 cm.

Work out the length of the rectangle.

Rod A is x cm long. Rod B is 15 mm longer than rod A.

Write an expression, in mm, for the length of rod B.

Tom is t years old. His sister is 4 years younger than Tom. His father is 3 times as old as Tom.

1. Write an expression for the sister's age.
2. Write an expression for the father's age.
3. The sum of the three ages is 51. Form an equation in t and solve it.

A plumber charges £40 as a call-out fee plus £25 for each hour of work.

1. Write a formula for the total cost, C pounds, for h hours of work.
2. Use your formula to work out the cost of 3.5 hours of work.

The angles of a quadrilateral are x°, (x + 30)°, (2x − 10)° and 100°.

Work out the size of the largest angle of the quadrilateral.

A plumber charges a fixed call-out fee of £40 plus £28 for each hour of work.

The plumber works for h hours on a job.

The total charge for the job is £C.

Write a formula for C in terms of h.

Priya thinks of a number.

She multiplies the number by 4 and then subtracts 9.

Her answer is 35.

Work out the number Priya thought of.

Rectangle A has length 8 cm and width (x + 2) cm.

Rectangle B has length 12 cm and width x cm.

The two rectangles have equal areas.

Work out the area of rectangle A.

Three consecutive whole numbers add up to 111.

Let the smallest number be n. Form an equation and solve it to find the three numbers.

Anna is a years old. Ben is 3 years older than Anna.

1. Write an expression for the sum of their ages in 2 years' time.
2. Show that this sum is always 7 more than twice Anna's age, whatever her age is.

A rectangle has length (3x + 2) cm and width (x + 1) cm. The perimeter is 54 cm.

Form an equation and solve it to find the length of the rectangle.

Tom is y years old.

His sister Freya is 7 years older than Tom.

1. Write down an expression, in terms of y, for Freya's age.
2. The sum of Tom's age and Freya's age is 23 years.
   Work out Tom's age.

A square has sides of length (x + 3) cm.

Another square has sides of length x cm.

The area of the larger square is 45 cm² more than the area of the smaller square.

Find the value of x.

A kite has two sides of length (2x + 1) cm and two sides of length (4x − 3) cm.

The perimeter of the kite is 44 cm.

Work out the length of one of the longer sides of the kite.

Two firms hire out a carpet cleaner.

• Firm A: £35 delivery charge plus £12 for each day
• Firm B: £20 delivery charge plus £15 for each day

1. Write a formula for the cost, £C, of hiring from Firm A for d days.
2. For how many days is the cost the same for both firms?

ABCD is a quadrilateral. AB is parallel to DC. Angle DAB = (4x + 5)° and angle ADC = (x + 60)°.

1. Explain why (4x + 5) + (x + 60) = 180.
2. Solve the equation to find x.
3. Work out the size of angle DAB.

A taxi journey costs a fixed charge of £3 plus £2 for each mile travelled.

A journey of m miles costs £C in total.

1. Write a formula for C in terms of m.
2. A journey costs £25 in total.
   Work out the number of miles travelled.

Three parcels have a total mass of 26 kg.

Parcel A has mass x kg.

Parcel B has mass (2x + 1) kg.

Parcel C has mass (3x − 5) kg.

Work out the mass of the heaviest parcel.

A box contains only red counters, blue counters and green counters.

The number of blue counters is twice the number of red counters.

The number of green counters is 9 more than the number of red counters.

There are 49 counters in the box altogether.

Work out the ratio of red counters to green counters. Give your answer in its simplest form.

A rectangle has length (2x + 5) cm and width (x + 2) cm.

The perimeter of the rectangle is 38 cm.

Work out the area of the rectangle.

Cuboid A measures 2 cm by 5 cm by x cm.

Cuboid B measures 4 cm by 5 cm by (x − 3) cm.

The two cuboids have equal volumes.

Find the value of x.

A triangle has a base of (x + 4) cm and a perpendicular height of x cm. Its area is 30 cm².

Form an equation, solve it, and work out the base of the triangle.

A cuboid has a base measuring x cm by (x + 3) cm and a height of 4 cm. Its volume is 160 cm³.

1. Show that x² + 3x - 40 = 0.
2. Solve the equation to find x.
3. Work out the surface area of the cuboid.

1. x, (x + 6) and 3x are three consecutive terms of an arithmetic sequence. Find x.
2. 3, x and 12 are three consecutive terms of a geometric sequence with a positive common ratio. Find x.