A number of girls form a singing group. All but 3 of the girls are blondes, all but 4 are brunettes, and all but 5 are redheads. How many girls are in the group?
x = total girls in group
x - 3 = blonds
x - 4 = brunettes
x - 5 = redheads
(x - 3) + (x - 4) + (x - 5) = x
3x - 12 = x
2x = 12
x = 6
1 redhead
2 brunettes
3 blond
To find out how many girls are in the singing group, we can follow a step-by-step approach using logical deductions based on the given information.
Let's assume the total number of girls in the group is represented by the variable "x".
From the given information:
1. "All but 3 of the girls are blondes" implies that the number of non-blonde girls is 3. So, we subtract 3 from the total number of girls: x - 3.
2. "All but 4 are brunettes" implies that the number of non-brunette girls is 4. So, we subtract 4 from the previous result: (x - 3) - 4 = x - 7.
3. "All but 5 are redheads" implies that the number of non-redhead girls is 5. So, we subtract 5 from the previous result: (x - 7) - 5 = x - 12.
Therefore, the equation representing the given information is x - 12 = 0.
To solve for x, we add 12 to both sides of the equation:
x - 12 + 12 = 0 + 12,
which simplifies to:
x = 12.
Hence, there are 12 girls in the singing group.