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Algebra Level 2

If the sum of 5 consecutive integers is A A , what is the sum of the next 5 consecutive integers?

A + 5 A + 5 A + 10 A + 10 A + 20 A + 20 A + 25 A + 25 A + 15 A + 15 A A A + 30 A + 30

Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

Rick B
Jan 29, 2015

Let these 5 5 consecutive integers be a a , b b , c c , d d and e e

We have a + b + c + d + e = A a+b+c+d+e = A

The sum of the next 5 5 consecutive integers is ( a + 5 ) + ( b + 5 ) + ( c + 5 ) + ( d + 5 ) + ( e + 5 ) = A + 25 (a+5)+(b+5)+(c+5)+(d+5)+(e+5) = \boxed{A+25}

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Very Simple :)

Chung Kevin - 6 years, 4 months ago

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Thx. I just posted this solution because it's simpler than the most common way, which is:

a + ( a + 1 ) + ( a + 2 ) + ( a + 3 ) + ( a + 4 ) = A a+(a+1)+(a+2)+(a+3)+(a+4) = A

⟹ ( a + 5 ) + ( a + 6 ) + ( a + 7 ) + ( a + 8 ) + ( a + 9 ) = A + 25 \implies (a+5)+(a+6)+(a+7)+(a+8)+(a+9) = A + 25

Rick B - 6 years, 4 months ago

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yes, that is the way I think most people would approach it.

Chung Kevin - 6 years, 4 months ago
Ramiel To-ong
Jul 31, 2015

First equation: A = 5X + 10 Second equation: 5x + 35 = Z Equating the 2 equations leads to Z = A + 25

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