Numbers

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Andrew thinks of Four consecutive numbers.The sum of the first 3 numbers is 100 more than the fourth number.What is the sum of these four consecutive numbers ?


The answer is 206.

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2 solutions

Jack Rawlin
Dec 25, 2014

Four consecutive number can be written as

a , a + 1 , a + 2 , a + 3 a, a+1, a+2, a+3

Since the sum of the first three is 100 100 more than the last one we can say that

a + ( a + 1 ) + ( a + 2 ) = ( a + 3 ) + 100 a + (a+1) + (a+2) = (a+3) + 100

This simplifies down to

3 a + 3 = a + 103 3a + 3 = a + 103

Re-arranging this gives us a value for a a

a = 50 a = 50

So the sum of the four numbers comes to

50 + 51 + 52 + 53 = 206 50 + 51 + 52 + 53 = 206

Venture Hi
Oct 20, 2014

The consecutive numbers can be written as follows: x, x+1, x+2, x+3 If the sum of the first 3 consecutive is a 100 more than the 4th, then x+x+1+x+2=x+3+100 x=50 Hence, the numbers are 50, 51,52,53

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