A machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than \( \frac{1}{4} \) the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is

To find the length of the bigger piece, we can set up an equation based on the information given. Let the length of the larger piece be \( x \) meters. According to the problem, the length of the smaller piece is 12 meters, which is also given as 5 meters greater than \( \frac{1}{4} \) the length of the larger piece. This can be expressed as: \( 12 = \frac{1}{4} x + 5 \) Now, subtracting 5 from both sides gives us: \( 7 = \frac{1}{4} x \) Multiplying both sides by 4 leads to: \( x = 28 \) So, the length of the bigger piece is **28 meters**. Here's a fun fact: Did you know that carpet manufacturing dates back thousands of years, originating from central Asia? The art of weaving carpets involves both practical craftsmanship and intricate designs, often telling stories or representing significant cultural symbols! Another interesting tidbit is that in the early days, carpets were used primarily by nomads for warmth and shelter. Today, they not only provide comfort underfoot but also serve aesthetic purposes, transforming living spaces into cozy environments.