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Home > Maths I > Relationships > Formulae

Maths I

Formulae

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Forming an equation

Example

Look at the following worked example.

Anwar, Ben and Colin all collect foreign coins.

Anwar has three times as many coins as Ben.

Colin has 8 coins more than Ben.

Ben has x coins.

Write down, in terms of x, the number of coins Anwar has and the number of coins Colin has.

Anwar has 3x (3 times x)

Colin has x + 8 (8 more than Ben)

If the three boys have 93 coins altogether, write down an equation and solve it for x.

Lots of foreign coins.

x + 3x + x + 8 = 93

Therefore,

5x + 8 = 93 is the equation.

5x = 85

x = 17

Write down the number of coins each boy has.

Ben has 17, Anwar has 51 and Colin has 25 (Check 17 + 51 + 25 equals 93).

Now try the following questions using the information given below.

Question

Three sisters, Ria, Sara and Tara are saving for a holiday.

Sara has twice as much money as Ria.

Tara has \pounds{5} less than Ria.

Ria has\pounds{x}.

Write down in terms of \;{x} how much money Sara has and how much money Tara has.

Answer

Sara has \pounds{2x} and Tara has \pounds{(x - 5)}

Question

The three girls have \pounds{59} altogether.

Write down an equation and solve it for \;x.

Answer

x + 2x + x - 5 = 59,

Therefore,

4x - 5 = 59, 4x = 64, x = 16

Question

Write down how much money each girl has.

Answer

Ria has \pounds{16}, Sara has \pounds{32}, Tara has \pounds{11} (Check: 16 + 32 + 11 = 59)

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