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
Step 1: Determine the fraction of people who drank mango juice. Let the total number of people be T. Fraction of people who drank mango juice = (3)/(8). Step 2: Determine the fraction of people remaining after those who drank mango juice. Remainder = 1 - (3)/(8) = (8)/(8) - (3)/(8) = (5)/(8) of the total people. Step 3: Determine the fraction of people who drank pineapple juice. Fraction of people who drank pineapple juice = (1)/(4) of the remainder. = (1)/(4) × (5)/(8) = (5)/(32) of the total people. Step 4: Determine the fraction of people who drank orange juice. The rest drank orange juice. Fraction of people who drank orange juice = Remainder - Fraction for pineapple juice = (5)/(8) - (5)/(32) To subtract these fractions, find a common denominator, which is 32. (5)/(8) = (5 × 4)/(8 × 4) = (20)/(32) So, the fraction for orange juice = (20)/(32) - (5)/(32) = (15)/(32) of the total people. Step 5: Use the given number of people who drank orange juice to find the total number of people (T). We are given that 240 people drank orange juice. (15)/(32) × T = 240 To find T, multiply 240 by the reciprocal of (15)/(32): T = 240 × (32)/(15) T = (240 ÷ 15) × 32 T = 16 × 32 T = 512 So, there were 512 people in total at the ceremony. Step 6: Calculate the number of people who drank mango juice. Number of people who drank mango juice = (3)/(8) of the total people. = (3)/(8) × 512 = 3 × (512 ÷ 8) = 3 × 64 = 192 The number of people who drank mango juice is 192. Last free one today — make it count tomorrow, or type /upgrade for unlimited.