question

A bag of sweets contains mints and toffees only.
There are 21 mints in the bag.
One quarter of the sweets are toffees.
Calculate the total number of sweets in the bag.

Let x = mints

Let y = toffees

Let s = the total number of sweets in the bag.

\(\begin{array}{|rcll|} \hline s &=& x + y \quad & | \quad x = 21 \\ s &=& 21 + y \quad & | \quad y = \frac14 s \\ s &=& 21 + \frac14 s \quad & | \quad \cdot 4 \\ 4s &=& 4\cdot 21 + s \quad & | \quad -s \\ 4s - s &=& 4\cdot 21 \\ 3s &=& 4\cdot 21 \quad & | \quad :3 \\ s &=& \frac{4\cdot 21}{3} \\ s &=& 4\cdot 7 \\ s &=& 28 \\ \hline \end{array}\)

There are 28  sweets in the bag.

21 mints and (28-21) = 7 toffees.

If 1/4 of the sweets are Toffees, then 3/4 are mints.

Let x= total sweets:     3/4 x = 21 mints     (solve for 'x')     then x = 21(4/3) = 28