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There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
------NOW ONTO THE QUESTION------------------------------
When 16x is divided by y, the quotient is x, and the remainder is 4. Applying the above rule, we can write: 16x = (y)(x) + 4 Subtract xy from both sides: 16x - xy = 4 Factor: x(16 - y) = 4
Since x and (16 - y) are both positive integers, there are 3 possible solutions: #1: x = 1 and (16 - y) = 4, in which case y = 12 #2: x = 2 and (16 - y) = 2, in which case y = 14 #3: x = 4 and (16 - y) = 1, in which case y = 15
What is the sum of all possible y-values? SUM = 12 + 14 + 15 = 41