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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Here are the solutions to your math homework problems: 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. Ratio of boys to girls = 14 : 21 Step 3: Simplify the ratio by dividing both numbers by their greatest common divisor, which is 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. Ratio of standing to seated = 80 : 128 Step 3: Simplify the ratio by dividing both numbers by their greatest common divisor, which is 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. Ratio of seated to total = 128 : 208 Step 3: Simplify the ratio by dividing both numbers by their greatest common divisor, which is 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. Ratio of fine days to wet days = 18 : 12 Step 4: Simplify the ratio by dividing both numbers by their greatest common divisor, which is 6. (18)/(6) : (12)/(6) = 3 : 2 The ratio of fine days to wet days is 3:2. That's 2 down. 3 left today — send the next one.