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Algebra Difficulty 2.2 Junior Find the answer

In the list 2,x,y,52, x, y, 5, the sum of any two adjacent numbers is constant. What is the value of xyx-y?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the sum of any two adjacent numbers is constant, then 2+x=x+y2 + x = x + y. This means that y=2y = 2 and makes the list 2,x,2,52, x, 2, 5. This means that the sum of any two adjacent numbers is 2+5=72 + 5 = 7, and so x=5x = 5. Therefore, xy=52=3x - y = 5 - 2 = 3.

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