Question 833352
Hi!
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Since the four integers are consecutive, let us call them x, x + 1, x + 2, and x + 3, where x + 3 is the greatest integer and x is the smallest.
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As we know that "the greatest of four consecutive integers is equal to five less than three times the smallest of these integers," we can make the following equation:
greatest integer = 3*(smallest integer) - 5
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Now plug in the variable expressions that we came up in the first step:
x + 3 = 3x - 5
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Now solve for x:
x + 8 = 3x
8 = 2x
2x = 8
x = 4
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Since the greatest integer x + 3, just plug in 4 for x: 4 + 3 = 7.
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Therefore, the value of the greatest of the consecutive integers is 7.
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I hope this helped!