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 define the number Liam started with as ( x ). According to the problem, he performs the following operations:

1. Multiplies the number by 5: ( 5x )
2. Subtracts 60 from the result: ( 5x – 60 )
3. This result equals the number he started with: ( 5x – 60 = x )

Now, we can solve the equation ( 5x – 60 = x ) step-by-step.

Step 1: Move ( x ) to the left side.

[

5x – x – 60 = 0

]

This simplifies to:

[

4x – 60 = 0

]

Step 2: Add 60 to both sides.

[

4x = 60

]

Step 3: Divide both sides by 4.

[

x = 15

]

So, the number Liam started with is 15.

Explanation: We set up an equation based on the operations Liam performed, solved the equation to isolate ( x ), and found that the number is 15.