A 36 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