SOLUTION: The units digit of a number is 4 times the tens digit. If 54 is added to the number, the digits will be interchanged. Find the number.

Question 658460: The units digit of a number is 4 times the tens digit. If 54 is added to the number, the digits will be interchanged. Find the number.
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
Let x by the tens digit and y be the units digit. Then from the first sentence:
y = 4x
And from the second sentence:
10x + y + 54 = 10y + x
Substituting y = 4x into the second equation gives:
10x + 4x + 54 = 10*(4x) + x
Combining like terms:
14x + 54 = 41x
Subtracting 14x from both sides and reversing the equation:
27x = 54
Dividing both sides by 27:
x = 2
So x = 2, y = 4*2 = 8, and the number is 28. 28 + 54 = 82
RELATED QUESTIONS
In a two digit number , the digit at unit's place is equal to the square of the digit at... (answered by pmatei)

25. The sum of the tens and hundreds digits of a three-digit number is 12. The units... (answered by ptaylor)

the sum of the digits of a three digit number is 14. The hundreds digit being 4 times the (answered by mananth)

The units digit is 1 more than 3 times the tens digit in a two digit number. The number... (answered by ankor@dixie-net.com)

the units digit of a two digit number is 4 times the tens digit. If the digits are... (answered by checkley75)

The units digit of a two-digit number exceeds the tens digit by 2. Find the number if it... (answered by stanbon)

The units� digit of a two-digit number is 7 more than the tens� digit. If 26 is added to... (answered by math_helper)

A three digit number is equal to 17 times the sum of its digit If 198 is added to the... (answered by Alan3354)

A three digit number is equal to 17 times the sum of its digit� If 198 is added to the... (answered by stanbon)