Answer :
The original bill amount should be £27.
Let's define the two-digit number where the tens digit is x and the units digit is y.
According to the problem, the sum of the digits is 9: x + y = 9.
The original number can be expressed as 10x + y.
If the digits are interchanged, the new number will be 10y + x.
The new number overcharges the customer by 45: (10y + x) - (10x + y) = 45.
- Solving the Equations:
Now, let's solve these equations step-by-step:
From the given sum of the digits: x + y = 9. (Equation 1)
From the overcharge equation: (10y + x) - (10x + y) = 45
Simplify the overcharge equation: 10y + x - 10x - y = 45
This simplifies to: 9y - 9x = 45, which simplifies further to: y - x = 5. (Equation 2)
- Now we have two equations:
x + y = 9
y - x = 5
- Adding these two equations eliminates x:
(x + y) + (y - x) = 9 + 5
This gives: 2y = 14
Therefore, y = 7
- Substitute y back into Equation 1:
x + 7 = 9
Therefore, x = 2
The original number is 10x + y = 10*2 + 7 = 27.
