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Question 1170802: Good day please may you assist me in the following question.
Consider the integers x and y. when y is divided by x the remainder is 29. when y is divided by x/2, the remainder is 13. determine x.
Found 2 solutions by mahikab, math_tutor2020:
Answer by mahikab(11)   (Show Source):
You can put this solution on YOUR website! Given that when y is divided by x the remainder is 29.
=> y = q*x + 29, where q is quotient [1]
Also given that when y is divided by x/2, the remainder is 13.
=> y = p*x/2 + 13, where p is quotient [2]
So we can write, qx + 29 = px/2 + 13
Multiple both sides by 2, 2qx + 58 = px + 26
or, px - 2qx = 58 - 26
x(p - 2q) = 32
x = 32/(p - 2q) and this is the value of x.
You can choose selective values of p and q to get the integer value of x.
For example, assuming q = 0 and p = 1, x = 32
So from [2] above: y = 1*32/2 + 13 = 16 + 13 = 29
Now if you divide 29 by 16 (x/2), the remainder is 13 while if you divide 29 by 32, the remainder is 29.
So, the solution is:  , where q and p are quotients as assumed above.
Answer by math_tutor2020(3817) (Show Source):
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