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Zaid and Matias, two farmers, constructed a 792 -foot fence around their very large garden. If Zaid constructed 
20% more of the fence than Matias did, how many feet of the fence did Zaid construct?

Zaid and Matias, two farmers, constructed a 792792 -foot fence around their very large garden. If Zaid constructed 20% 20 \% more of the fence than Matias did, how many feet of the fence did Zaid construct?

Full solution

Q. Zaid and Matias, two farmers, constructed a 792792 -foot fence around their very large garden. If Zaid constructed 20% 20 \% more of the fence than Matias did, how many feet of the fence did Zaid construct?
  1. Denote Fence Length: Let's denote the length of the fence Matias constructed as MM feet. Since Zaid constructed 20%20\% more of the fence than Matias, Zaid constructed M+0.20MM + 0.20M feet of the fence.
  2. Combine Matias and Zaid: Combining Matias's and Zaid's portions, we get the total length of the fence: M+(M+0.20M)=792M + (M + 0.20M) = 792 feet.
  3. Simplify Equation: Combine like terms.\newlineM+M+0.20M=792M + M + 0.20M = 792\newline2.20M=7922.20M = 792 feet.
  4. Solve for M: To find the value of M, we need to divide 2.202.20 on both sides of the equation.\newlineM=792 feet2.20M = \frac{792 \text{ feet}}{2.20}\newlineM=360 feetM = 360 \text{ feet}
  5. Calculate Zaid's Portion: Now that we have Matias's portion, we can calculate Zaid's portion, which is 20%20\% more than Matias's.\newlineSo, Zaid's portion is M+0.20M=360M + 0.20M = 360 feet +0.20×360+ 0.20 \times 360 feet.\newlineCalculation: Zaid's portion = 360360 feet +72+ 72 feet = 432432 feet