If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number? A.250,250
B.315,185
C.370,230
D.410,90
E.480,20
2 answers:
Let x be the first digit (ten's place) of the original number. Let y be the second digit (one's place) of the original number. (x + y)7 = original number (x + y)7 = 10x + y 7x + 7y = 10x + y 6y = 3x 10y + x = (x + y) + 18 9y = 18 y = 2 6y = 3x 6(2) = 3x 12 = 3x x = 4 x is the first digit, and y is the second digit, so the original number is 42.
The answer is A. 42 Solution: Let x= ones digit, y=tens digit 1st condition (original number) : 7(x+y)=10y + x 2nd condition (new number by reversing the digits): 18+x+y=10x+y simplifying: 1st condition: 6x=3y 2nd condition: x=2 substituting x=2 to 6x=3y <span>y=4</span>
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