This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back — been a while! Let's pick up where you left off. Here's how to solve the problem: a) Represent the information on a Venn diagram. Let M be the set of farmers who grow maize and R be the set of farmers who grow rice. Given: Total farmers, n(U) = 80 Farmers who grow maize, n(M) = 50 Farmers who grow rice, n(R) = 60 Let x be the number of farmers who grow both crops, n(M R) = x. The regions in the Venn diagram are: • Farmers who grow only maize: n(M only) = n(M) - n(M R) = 50 - x • Farmers who grow only rice: n(R only) = n(R) - n(M R) = 60 - x • Farmers who grow both maize and rice: n(M R) = x The Venn diagram would show two overlapping circles. The left part of the maize circle (not overlapping) would be 50-x. The overlapping part would be x. The right part of the rice circle (not overlapping) would be 60-x. b) Write an equation in x and solve it. The total number of farmers is the sum of farmers in each distinct region of the Venn diagram. n(U) = n(M only) + n(R only) + n(M R) Substitute the expressions for each region: 80 = (50 - x) + (60 - x) + x Combine like terms: 80 = 50 + 60 - x - x + x 80 = 110 - x Now, solve for x: x = 110 - 80 x = 30 The number of farmers who grow both crops is 30. Send me the next one 📸