Forming and solving equations

Make y the subject of w = 3 y – d

Diego buys b boxes of crayons and p packets of crayons.

There are 12 crayons in each box. There are 3 crayons in each packet.

Diego buys a total of T crayons.

Write down a formula for T in terms of b and p

Kye has some toy cars.

He has n red cars. He has twice as many blue cars as red cars. He has 7 more green cars than red cars.

Write an expression, in terms of n, for the total number of red cars, blue cars and green cars that Kye has. Write your answer in its simplest form.

The total number of cars that Kye has is T

Write an expression, in terms of T and n, for the number of cars that Kye has that are not red cars, blue cars or green cars.

Here is a number machine.

When the input is 7 the output is 60

Work out the value of y

Here is a different number machine.

The input is x

Write down an expression, in terms of x, for the output.

Here is a number machine.

Work out the output when the input is 9

Here is a different number machine.

When the input is 30 the output is 18

Find a suitable way to complete the number machine.

The following rule is used to work out the total cost, in euros, of hiring a cement mixer.

James hires a cement mixer for 3 days.

Work out the cost to James of hiring the cement mixer.

The cost to Sophia of hiring a cement mixer is 61 euros.

For how many days does Sophia hire the cement mixer?

In a warehouse there are two types of shelves, type R and type S.

These two types of shelves are arranged into shelving units that form a sequence of patterns.

Here are the first three terms in the sequence.

The width of each type R shelf is 2.4 m and the width of each type S shelf is 3.5 m

Work out the total width of a shelving unit that has 6 type R shelves.

A shelving unit has n type R shelves. The total width of this shelving unit is W metres.

Find an expression for W in terms of n Give your answer in its simplest form.

Molly uses this number machine to work out the amount of tax that she has to pay on the money she earns.

When Molly works n hours the amount of tax she has to pay is £T

Find a formula for T in terms of n

Alisa, Jena and Mikael each pick cucumbers.

Alisa picks C cucumbers. Jena picks 5 fewer cucumbers than Alisa. Mikael picks twice as many cucumbers as Alisa.

The total number of cucumbers picked by Alisa, Jena and Mikael is T

Find a formula for T in terms of C Give your formula in its simplest form.

Factorise 6 x – 15

There are 200 bolts in each box of bolts. Samira buys c boxes of bolts.

Samira uses the bolts she bought to fill packets of bolts. There are 50 bolts in each packet of bolts. Samira sells d packets of bolts.

The total number of bolts Samira has left is T

Write down a formula for T in terms of c and d

Here is a number machine.

Work out the output when the input is 7

Work out the input when the output is 160

When the input is n, the output is P.

Find a formula for P in terms of n.

c = 4 d = 7

Work out the value of 3c + 2d

p = −6 m = −2

Work out the value of 2p² + 3m

There are 6 eggs in a small box of eggs. There are 12 eggs in a large box of eggs.

Alex buys g small boxes of eggs and h large boxes of eggs. He buys a total of T eggs.

Write down a formula for T in terms of g and h.

The diagram shows a regular hexagon, ABCDEF, and an isosceles triangle, GHJ.

The perimeter of the hexagon is equal to the perimeter of the triangle.

Find the length of each side of the hexagon. Show clear algebraic working.

Here is a sequence of patterns made from circles.

number 1
number 2
number 3
number 4

In the space below, draw Pattern number 5

Complete the table.

Work out the number of circles in Pattern number 8

C is the number of circles in Pattern number P

Write down a formula for C in terms of P

A different sequence of patterns is made from triangles. The rule to find the number of triangles in each pattern is

multiply the Pattern number by 5 and subtract 4

Is there a pattern in this sequence that is made from exactly 136 triangles? You must give a reason for your answer.

Expand x (5 – x)

Factorise 3y – 21

Make p the subject of the formula f = 3p – d

Sergio buys m boxes of seeds and n packets of seeds.

Each box contains 10 seeds. Each packet contains 6 seeds.

The total number of seeds that Sergio buys is T.

Write down a formula for T in terms of m and n.

Three tins, A, B and C, each contain buttons.

Tin A contains x buttons. Tin B contains 4 times the number of buttons that tin A contains. Tin C contains 7 fewer buttons than tin A.

The total number of buttons in the three tins is 137

Work out the number of buttons in tin C.