Question

Julie and Liam write down the same number.

Julie multiplies the number by 5 and then adds 4 to the result.
She writes down her answer.

Liam subtracts the number from 10
He writes down his answer.

Julie's answer is two thirds of Liam's answer.

Work out the number that Julie and Liam started with.
You must show your working.

Answer 1

Given :- Julie and Liam write down the same number. Julie multiplies the number by 5 and then adds 4 to the result.

She writes down her answer. Liam subtracts the number from 10 He writes down his answer. Julie's answer is two thirds of Liam's answer.

Solution :-

Let Julie and Liam write down the same number as x .

So,

→ Answer of Julie = multiplies the number by 5 and then adds 4 = (5x + 4)

and,

→ Answer of Liam = subtracts the number from 10 = (10 - x)

A/q,

→ Julie's answer = (2/3) of Liam's answer.

→ (5x + 4) = (2/3)(10 - x)

→ 15x + 12 = 20 - 2x

→ 15x + 2x = 20 - 12

→ 17x = 8

→ x = (8/17)

verification :-

→ (8/17) * 5 + 4 = (2/3)(10 - 8/17)

→ 40/17 + 4 = (2/3) * (162/17)

→ 108/17 = 108/17

therefore, the number that Julie and Liam started with is (8/17) .

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