SOLUTION: 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

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): You can put this solution on YOUR website!

The problem has been previously answered here
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1170970.html
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