A36 foot long roll of banner material must be cut into three pieces with no material left over to make three banners. the second banner must be 4 feet longer than the first banner in the third banner must be also 4 feet longer than the second. how long should each banner be

The length of the first banner = 8 ft

The length of the second banner = 12  ft

The length of the third banner  = 16 ft

Step-by-step explanation:

The total length of the banner material = 36 ft

Now, let us assume the length of the first banner  = k ft

So, the length of the second banner  = First banner + 4 ft = ( k + 4) ft

The length of the third banner = Second banner  + 4 ft  = [( k + 4) + 4]  ft

Now, according to the question:

The length of ( First  + Second + Third) banner  = 36 ft

⇒ (k) + (k +4) + (k + 8)  = 36

or, 3 k = 36 - 12= 24

or, k = 24/3  = 8

⇒ k = 8 ft

So, the length of the first banner = k = 8 ft

The length of the second banner = k + 4 = 8 + 4 = 12  ft

The length of the third banner = k + 4 + 4  = 8 + 8 =  16 ft

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