AlgebraVery hardClass size from fractions of two groups
Algebra practice question
In a class, three quarters of the boys and half of the girls play a musical instrument. If 18 boys and 12 girls play an instrument, how many pupils are in the class?
Answer: 48
(3/4)b = 18 gives b = 24, and (1/2)g = 12 gives g = 24, so the class has 48 pupils.
Common wrong answers
- If you answered 30
- 30 is the number who play, not the class size.
- If you answered 36
- 36 is 24 + 12, mixing the girls who play with the total boys.
- If you answered 40
- 40 comes from a slip in one of the two divisions.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.