1. **State the problem:** Eva and Dexter share sweets in the ratio 1:2. Mo and Annie share the same total number of sweets as Eva and Dexter, but in the ratio 3:5. 2. **Part a:** If Eva gets $x$ sweets, Dexter gets sweets in ratio 2 to Eva's 1, so Dexter gets: $$\text{Dexter's sweets} = 2x$$ 3. **Part b:** Mo and Annie share sweets in ratio 3:5. If Mo gets $3y$ sweets, then Annie gets: $$\text{Annie's sweets} = 5y$$ 4. **Part c i):** Total sweets Eva and Dexter have: $$x + 2x = 3x$$ Total sweets Mo and Annie have: $$3y + 5y = 8y$$ Since they have the same total sweets: $$3x = 8y$$ 5. **Part c ii):** From $3x = 8y$, solve for $y$: $$y = \frac{3x}{8}$$ Or equivalently: $$\frac{3}{8}x = y$$ 6. **Part d:** Find the ratio of Eva's : Dexter's : Mo's : Annie's sweets. Eva = $x$ Dexter = $2x$ Mo = $3y = 3 \times \frac{3x}{8} = \frac{9x}{8}$ Annie = $5y = 5 \times \frac{3x}{8} = \frac{15x}{8}$ To clear denominators, multiply all by 8: Eva: $8x$ Dexter: $16x$ Mo: $9x$ Annie: $15x$ Divide all by $x$ (assuming $x \neq 0$): $$8 : 16 : 9 : 15$$ Simplify by dividing by 1 (no common factor for all four): $$8 : 16 : 9 : 15$$ **Final ratio:** $8 : 16 : 9 : 15$