Substitution and Formulae

P = 2g + 3h

Work out the value of P when g = 7 and h = −4

P = ....................

Answer explanation

P = 2(7) + 3(-4)

P = 2

Simon has x sweets.
Yuen has 2 more sweets than Simon.
Giulia has 3 times as many sweets as Yuen.

Simon, Yuen and Giulia have a total of T sweets.

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Write down a formula for T in terms of x.

Give your formula in its simplest form.​ ​ ​

Answer explanation

Simon = x

Yuen = x + 2

Giulia = 3(x + 2) = 3x + 6

Simon + Yuen + Giulia

= x + x + 2 + 3x + 6

= 5x + 8

Make g the subject of the formula :​  

r = 4g + 7

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P = 2a + 3b

Work out the value of P when a = 5 and b = 8

P = ...........................................................

Answer explanation

P = 2(5) + 3(8)

P = 34

P = 2a + 3b

Work out the value of a when P = 16 and b = 20

a = ...........................................................

Answer explanation

16 = 2a + 3(20)

16 = 2a + 60

-44 = 2a

-22 = a

a = -22

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.

Answer explanation

T = m x 10 + n x 6

T = 10m + 6n

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

TOTAL COST = 8 euros per day plus 5 euros

James hires a cement mixer for 3 days.

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

.............. euros

Answer explanation

Total Cost = 8 x 3 + 5

Total Cost = 29 euros

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

TOTAL COST = 8 euros per day plus 5 euros

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

For how many days does Sophia hire the cement mixer?

 ........................................................... days

Here is a number machine.

When the input is 15, the output is...........

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