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.
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
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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.