text: Krzychau1
  
  2021-12-16
  
  A 20-foot board is to be cut into two pieces whose lengths are in the ratio of 7 to 3. Find the lengths of the two pieces.
  
  Bernard Lacey
  
  Expert
  
  Step 1 Given- A board of length 20 foot.
  To find- The length of two pieces, if it cut into the ratio 7:3.
  Step 2
  Explanation- As per the question, the length of the board is 20 foot, and it cut into two pieces in the ratio of 7:3.
  As the total length of the board is 20, and it must be equal to the length of the two pieces, so we have to multiply with such such number in the ratio whose sum is 20, so multiplying by 2, we get,
  $=7\cdot 2+3\cdot 2$
  $=14+6$
  $=20$
  That is equal to the total length of the board.
  So, the length of the two pieces are 14 feet and 6 feet.
  Answer- Hence, the length of the two pieces are 14 feet and 6 feet.
  
  Cheryl King
  
  Expert
  
  A 20 foot board is cut into two pieces whose lengths are in the ration of 7 to 3. Find the length of the longer piece.
  7 to 3 is the same as 7x to 3x where 7x is the longer piece.
  Equation:
  $7x+3x=20ft$
  $10x=20$
  $x=2$
  longer piece $=7x=7\cdot 2=14ft$
  
  nick1337
  
  Expert
  
  Step 1
  Let x denote the length of one piece of the board in feet.
  Since the two pieces of the board are in the ratio of 7 to 3, it follows that the other piece has a length of $\frac{7}{3}x$ in feet.
  Given the total length equal to 20 feet, an equation can be set-up as shown below.
  $x+\frac{7}{3}x=20$
  Step 2
  Multiply by 3 on both sides of the equation.
  $3\left(x+\frac{7}{3}x\right)=3×20$
  3x+7x=60
  10x=60
  Divide throughout by 10 to get,
  $\frac{10x}{10}=\frac{60}{10}$
  x=6
  Step 3
  If x=6, then we have
  $\frac{7}{3}x=\frac{7}{3}×6$
  =14
  Therefore, the lengths of the two pieces are 6 feet and 14 feet.
  
  Do you have a similar question?
explanation: The document contains a math problem and multiple solutions provided by different experts. The problem is to find the lengths of two pieces of a 20-foot board that are cut in the ratio of 7 to 3. Each expert provides a step-by-step solution to the problem, and the final answer is consistently that the lengths of the two pieces are 14 feet and 6 feet.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Krzychau1
  
  2021-12-16
  
  A 20-foot board is to be cut into two pieces whose lengths are in the ratio of 7 to 3. Find the lengths of the two pieces.
  
  Bernard Lacey
  
  Expert
  
  Step 1 Given- A board of length 20 foot.
  To find- The length of two pieces, if it cut into the ratio 7:3.
  Step 2
  Explanation- As per the question, the length of the board is 20 foot, and it cut into two pieces in the ratio of 7:3.
  As the total length of the board is 20, and it must be equal to the length of the two pieces, so we have to multiply with such such number in the ratio whose sum is 20, so multiplying by 2, we get,
  $=7\cdot 2+3\cdot 2$
  $=14+6$
  $=20$
  That is equal to the total length of the board.
  So, the length of the two pieces are 14 feet and 6 feet.
  Answer- Hence, the length of the two pieces are 14 feet and 6 feet.
  
  Cheryl King
  
  Expert
  
  A 20 foot board is cut into two pieces whose lengths are in the ration of 7 to 3. Find the length of the longer piece.
  7 to 3 is the same as 7x to 3x where 7x is the longer piece.
  Equation:
  $7x+3x=20ft$
  $10x=20$
  $x=2$
  longer piece $=7x=7\cdot 2=14ft$
  
  nick1337
  
  Expert
  
  Step 1
  Let x denote the length of one piece of the board in feet.
  Since the two pieces of the board are in the ratio of 7 to 3, it follows that the other piece has a length of $\frac{7}{3}x$ in feet.
  Given the total length equal to 20 feet, an equation can be set-up as shown below.
  $x+\frac{7}{3}x=20$
  Step 2
  Multiply by 3 on both sides of the equation.
  $3\left(x+\frac{7}{3}x\right)=3×20$
  3x+7x=60
  10x=60
  Divide throughout by 10 to get,
  $\frac{10x}{10}=\frac{60}{10}$
  x=6
  Step 3
  If x=6, then we have
  $\frac{7}{3}x=\frac{7}{3}×6$
  =14
  Therefore, the lengths of the two pieces are 6 feet and 14 feet.
  
  Do you have a similar question?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem and multiple solutions provided by different experts. The problem is to find the lengths of two pieces of a 20-foot board that are cut in the ratio of 7 to 3. Each expert provides a step-by-step solution to the problem, and the final answer is consistently that the lengths of the two pieces are 14 feet and 6 feet.
  
  Label: multiple-question-and-answer