Question

In a set of $216$ marbles, there are $x$ black marbles and $y$ white marbles. If the number of white marbles is $7$ times the number of black marbles, how many black marbles are there?

• A. $56$
• B. $27$
• C. $32$
• D. $189$

Answer 1

The correct option is B $27$

Total number of marbles = 216
Number of black marbles $=x$
Number of white marbles $=y$

Case 1: Number of white marbles $=7\times$ Number of black marbles
So, $y=7\times x$

$\Rightarrow y=7x$

Case 2: Total number of marbles $=216$
Hence,
Number of black marbles $+$ Number of white marbles$=216$
$\Rightarrow x+y=216$

From Case $1$, $y=7x$ and from Case $2$, $x+y=216$
So, we can write Case $2$, as
$x+7x=216$
$8x=216$
Dividing both side by $8$, we get
$x=\frac{216}{8}$
$x=27$

So, $y=7x=7\times 27=189$
Answer:
Number of black marbles $=27$,
Number of white marbles $=189$