A bag of sweets contains only mints, sherberts and toffees - OCR - GCSE Maths - Question 6 - 2019 - Paper 4

Next, we introduce the number of toffees. Let the number of toffees be $y$. According to the ratio given, we have:

$\frac{3x}{y} = \frac{7}{5}$

This implies that $3x \cdot 5 = 7y$, leading to:

$y = \frac{15x}{7}$.

Now, let's calculate the total number of sweets in the bag:

$\text{Total} = 2x + 3x + y = 2x + 3x + \frac{15x}{7} = 5x + \frac{15x}{7} = \frac{35x}{7} + \frac{15x}{7} = \frac{50x}{7}$.

Finally, we calculate the fraction of the sweets that are sherberts:

$\text{Fraction of sherberts} = \frac{\text{Number of sherberts}}{\text{Total number of sweets}} = \frac{3x}{\frac{50x}{7}} = \frac{3x \cdot 7}{50x} = \frac{21}{50}$.

Thus, the fraction of the sweets that are sherberts is ( \frac{21}{50} ).