The 5 (FIVE) consecutive integers are: 52, 53, 54, 55, and 56 .
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The expression is written as:
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x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 270 ;
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in which the 5 (FIVE) consecutive integers are:
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x, (x + 1), (x + 2), (x + 3), (x + 4) .
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To find the 5 (FIVE) consecutive integers, we solve for "x" , and the plug in the the value of "x" for the expressions of the other integers.
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We have:
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x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 270 ;
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Rewrite as:
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x + x + 1 + x + 2 + x + 3 + x + 4 = 270 ;
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Combine the "like terms" on the "left-hand side" of the equation:
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x + x + x + x + x = 1x + 1x + 1x + 1x = 1x = 5x ;
1 + 2 + 3 + 4 = 10 ;
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→ 5x + 10 = 270 ;
Subtract "10" from each side of the equation;
5x + 10 − 10 = 270 − 10 ;
to get:
5x = 260 ;
Divide EACH SIDE of the equation by "5" ;
5x / 5 = 260 / 5 ;
to get:
x = 52 ;
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x = 52 ;
x + 1 = 52 + 1 = 53 ;
x + 2 = 52 + 2 = 54 ;
x + 3 = 52 + 3 = 55 ;
x + 4 = 52 + 4 = 56 ;
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The 5 (FIVE) consecutive integers are: 52, 53, 54, 55, and 56 .
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Let us check our answer:
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52 + 53 + 54 + 55 + 56 =? 270 ?
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52 + 53 = 105;
105 + 54 = 159 ;
159 + 55 = 214 ;
214 + 56 = 270 ;
→ 52 + 53 + 54 + 55 + 56 =? 270 ? Yes!
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