At a drama CCA session, there are 48 students altogether. The ratio of boys to girls is 5 : 7. After the session ends, 4 more boys and 4 more girls join the CCA. What is the new ratio of boys to girls, in its simplest form?
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Worked Solution
Step 1: Find the value of 1 part using the total number of students.
Total parts = 5 + 7 = 12
1 part = 48 ÷ 12 = 4 students
Step 2: Find the current number of boys and girls.
Boys: 5 × 4 = 20
Girls: 7 × 4 = 28
Check: 20 + 28 = 48 ✓
Step 3: Add the new members.
New boys: 20 + 4 = 24
New girls: 28 + 4 = 32
Step 4: Find the greatest common factor (GCF) of 24 and 32.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
GCF = 8
Step 5: Simplify the ratio.
24 ÷ 8 = 3
32 ÷ 8 = 4
The new ratio of boys to girls is 3 : 4.
Correct answer: 3 : 4
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