jared has a wooden board 11 ft long. he wants to cut it into two pieces so that the longer piece is 4 ft less than 4 times the length of the shorter piece. how long will each piece of board be? enter your answers in the boxes.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The lengths of the shorter and longer pieces of a board should be determined.

the case

Let's say that the shorter parts are x in length.

as stated

Jared has an 11-foot wooden board with him.

In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.

The length of the longer pieces is then equal to 4x - 4.

The equation then becomes

[tex]x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft[/tex]

The shorter pieces will therefore be 3 feet long.

The longer pieces' length -

[tex]4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft[/tex]

The longer pieces will therefore be 8 feet long.

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