Jambmaths question:
Some white balls were put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white ball from the basket is $\tfrac{3}{7}$, how many white balls were introduced.
Option A:
12
Option B:
21
Option C:
28
Option D:
32
Jamb Maths Solution:
$\begin{align} & \text{Let the total number of balls be }x \\ & P(Red)=\frac{12}{x} \\ & P(Black)=\frac{16}{x} \\ & P(White)=\frac{3}{7} \\ & P(Red)+P(Black)+P(White)=1 \\ & 1=\frac{12}{x}+\frac{16}{x}+\frac{3}{7} \\ & \frac{12}{x}+\frac{16}{x}=1-\frac{3}{7} \\ & \frac{12}{x}+\frac{16}{x}=\frac{4}{7} \\ & \frac{12+16}{x}=\frac{4}{7} \\ & \frac{28}{x}=\frac{4}{7} \\ & x=\frac{28\times 7}{4}=49 \\ & \text{The number of white balls introduced}~=49(12+28)=21 \\\end{align}$
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