Liam thinks of a number. He multiplies the number by 5 and then subtracts 60 from the result. His answer equals the number he started with. What was the number Liam started with? Show your working. You may get a mark

Let’s denote the number Liam thinks of as ( x ). According to the problem, he multiplies this number by 5 and then subtracts 60, which equals the original number. We can write this as an equation:

[ 5x – 60 = x ]

Now, we can solve for ( x ):

1. First, add 60 to both sides of the equation:

[ 5x – 60 + 60 = x + 60 ]

[ 5x = x + 60 ]

2. Next, subtract ( x ) from both sides:

[ 5x – x = 60 ]

[ 4x = 60 ]

3. Now, divide both sides by 4 to solve for ( x ):

[ x = frac{60}{4} ]

[ x = 15 ]

So, the number Liam started with is ( 15 ).

Explanation: We set up an equation based on Liam’s operations and solved it step-by-step to find the original number. If you need more help, feel free to ask or check the extended services page for more in-depth assistance!