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A board, 77 cm long is cut into three pieces such that the second piece is twice as long as the first and the third 7 cm longer than the second. Find the length of the shorter piece. Cm

User Shj
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Given:

The length of the board is 77 cm.

Let a be the length of the first piece.

Let b be the length of the second piece.

Let c be the length of the third piece.

Given that the second piece is twice as long as the first.


b=2a

Given that the third is 7 cm longer than the second.


c=b+7

Substitute b=2a, we get


c=2a+7

The sum of the three pieces =The length of the board.


a+b+c=77

Substitute b=2a and c=2a+7, we get


a+2a+2a+7=77


5a+7=77

Subtracting 7 from both sides, we get


5a+7-7=77-7


5a=70

Dividing both sides by 5, we get


(5a)/(5)=(70)/(5)
a=14cm

Substitute a=14cm in b=2a and c=2a+7, we get


b=2*14=28cm
c=2*14+7=35cm

Hence the length of the shorter piece is 14cm.

User ZMacarozzi
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