Question

A piece of the string $175$ cm. in length was cut into two pieces, the ratio of whose length was $5:2$. Find the length of the smallest piece.

Answer 1

Let the length of the greatest piece be $x$

Therefore, the length of the smallest piece be $175-x$

According to the problem, we have

$\frac{x}{175-x}=\frac{5}{2}$

$2x=5(175-x)$

$2x=875-5x$

$7x=875$

$\therefore x=125$

Therefore, length of smallest piece is $175-x=175-125=50$ cm.