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Algebra Difficulty 4.0 AMC 10/12 Find the answer North Macedonia

Find the number by which the sum of the numbers 5486354863 and 3060830608 has to be decreased in order to obtain their difference?

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

Solution

We solve the equation (54863+30608)x=5486330608(54863 + 30608) - x = 54863 - 30608.

Its solution is x=8547124255=61216x = 85471 - 24255 = 61216.

The sum has to be decreased by 6121661216.

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