The original number is 64
Step-by-step explanation:
The given is:
- The sum of the digits of a two-digit number is 10
- When the digits are reversed the new number is 18 less than the original number
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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