The original number is 64
Step-by-step explanation:
The given is:
We need to find the original number
Assume that the unit digit of the number is x and the ten digit is y
∵ The unite digit of the number is x
∵ The ten digit of the number is y
∵ The sum of the two digits is 10
- Add x and y, then equate the sum by 10
∴ x + y = 10 ⇒ (1)
∵ The value of the number is x + 10y
- Reverse the digits means y will be the unit digit and x will
be the ten digit
∴ The new number is y + 10x
∵ The new number is 18 less than the original number
- That means their difference is 18, (the original number minus
the new number = 18)
∴ (x + 10y) - (y + 10x) = 18
- Simplify the left hand side
∴ x + 10y - y - 10x = 18
- Add the like terms in the left hand side
∴ -9x + 9y = 18
- Divide both sides by 9
∴ -x + y = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equation (1) and (2) to eliminate x
∴ 2y = 12
- Divide both sides by 2
∴ y = 6
- Substitute the value of y in equation (1) to find x
∵ x + 6 = 10
- Subtract 6 from both sides
∴ x = 4
∵ The original number is x + 10y
∵ x = 4 and y = 6
∴ The original number = 4 + 10(6) = 4 + 60 = 64
The original number is 64
To check the answer reverse the digits of the number
∵ The new number is y + 10x
∴ The new number = 6 + 10(4) = 6 + 40 = 46
∵ The original number is 64
∵ The new number is 46
∵ 64 - 46 = 18
∴ The new number is less than the original number by 18
Learn more:
You can learn more about the digits of a number in brainly.com/question/10754198
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