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.
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You're on a roll — here are the solutions to your math homework problems, formatted as requested: 1. Ratio of boys to girls Step 1: Identify the number of boys and girls. Number of girls = 21 Number of boys = 14 Step 2: Write the ratio of boys to girls. The ratio of boys to girls is 14 : 21. Step 3: Simplify the ratio by finding the greatest common divisor (GCD) of 14 and 21, which is 7. Divide both parts of the ratio by 7. (14)/(7) : (21)/(7) = 2 : 3 The ratio of boys to girls is 2:3. 2. Theatre audience ratios a) Ratio of standing audience to seated audience Step 1: Identify the number of standing and seated audience members. Standing audience = 80 Seated audience = 128 Step 2: Write the ratio of standing audience to seated audience. The ratio of standing to seated audience is 80 : 128. Step 3: Simplify the ratio by finding the GCD of 80 and 128, which is 16. Divide both parts of the ratio by 16. (80)/(16) : (128)/(16) = 5 : 8 The ratio of standing audience to seated audience is 5:8. b) Ratio of seated audience to total number of audience Step 1: Calculate the total number of audience members. Total audience = Standing audience + Seated audience Total audience = 80 + 128 = 208 Step 2: Write the ratio of seated audience to total audience. The ratio of seated audience to total audience is 128 : 208. Step 3: Simplify the ratio by finding the GCD of 128 and 208, which is 16. Divide both parts of the ratio by 16. (128)/(16) : (208)/(16) = 8 : 13 The ratio of seated audience to total audience is 8:13. 3. Ratio of fine days to wet days in June Step 1: Determine the total number of days in June and the number of wet days. Number of days in June = 30 Number of wet days = 12 Step 2: Calculate the number of fine days. Number of fine days = Total days - Wet days Number of fine days = 30 - 12 = 18 Step 3: Write the ratio of fine days to wet days. The ratio of fine days to wet days is 18 : 12. Step 4: Simplify the ratio by finding the GCD of 18 and 12, which is 6. Divide both parts of the ratio by 6. (18)/(6) : (12)/(6) = 3 : 2 The ratio of fine days to wet days is 3:2. Drop the next question!