If x is the remainder when 2312, 1417, and 1059 are all divided by y (where y is greater than one), find the value of y – x.
since the remainders are equal,
2312-1417 = 895
2312-1059 = 1253
1417-1059 = 358
are all multiples of y.
The GCF of those is 179.
Divide any of the given numbers by 179 and the remainder is 164.
So, y-x = 179-164 = 15
To find the value of y - x, first, we need to find the remainder when each of the given numbers is divided by y individually. Let's denote the remainders as x1, x2, and x3 for 2312, 1417, and 1059 respectively.
To find x1, we divide 2312 by y. Similarly, to find x2, we divide 1417 by y, and for x3, we divide 1059 by y.
The difference between y and x is given by y - x = y - (x1 + x2 + x3).
However, since all the given numbers have the same remainder (x) when divided by y, x1, x2, and x3 will all be equal to x. Therefore, we can rewrite the equation as y - x = y - (x + x + x).
Simplifying further, we have y - x = y - 3x.
Now, to find the value of y - x, we need more information.