SOLUTION: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?       Log On

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Question 3427: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?
(A) 23x + 17y =19
(B) 17x –23y = 9
(C) 17x +23y =19
(D) 14x + 5y = 6
(E) 5x – 14y = -6
Found 2 solutions by drglass, longjonsilver:
Answer by drglass(89) About Me  (Show Source):
You can put this solution on YOUR website!
n = 17x + 5 and

n = 23y + 14

are true statements. Therefore,

17x + 5 = 23y + 14

subtract 5 to both sides and you get 17x = 23y + 19

subtract 2y from both sides and you get 17x - 23y = 9

This is choice B

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
n/17 = x + 5/17 --> n = 17x + 5 --eqn1

n/23 = y + 14/23 --> n = 23y + 14 --eqn2

Subtract these 2, to give 17x+5 - (23y+14) = 0
17x+5-23y-14 = 0
17x-23y-9 = 0
17x-23y = 9

which is your answer B.

jon.