Question 16, 2.4.11
HW Score: $65 \%, 13$ of 20 points
Part 1 of 3
Points: 0 of 1
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A 20 -inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. If $x$ represents the length of the first piece, find the lengths of all three pieces
What is the length of the first piece?
Answer
Final Answer: The length of the first piece is \(\boxed{2}\) inches.
Step 1 ：The problem states that a 20-inch board is cut into three pieces. The first piece is x inches long, the second piece is 4 times as long as the first piece, and the third piece is 5 times as long as the first piece. This means that the total length of the board is the sum of the lengths of the three pieces.
Step 2 ：We can set up an equation to represent this relationship: \(x + 4x + 5x = 20\)
Step 3 ：Solving this equation gives us \(10x = 20\)
Step 4 ：Dividing both sides of the equation by 10 gives us \(x = 2\)
Step 5 ：Final Answer: The length of the first piece is \(\boxed{2}\) inches.
