Question: 1. A recipe uses flour and sugar in the ratio $5:3$. If $275$ g of flour is used, how much sugar is needed? [2 marks]
1. **State the problem:** We have a recipe where the ratio of flour to sugar is $5:3$. Given $275$ g of flour, we need to find the amount of sugar required.
2. **Formula and rules:** The ratio $5:3$ means for every $5$ parts of flour, there are $3$ parts of sugar.
3. **Set up the proportion:** Let the amount of sugar be $x$ grams. Then:
$$\frac{\text{flour}}{\text{sugar}} = \frac{5}{3} = \frac{275}{x}$$
4. **Solve for $x$:**
$$5x = 3 \times 275$$
$$5x = 825$$
$$x = \frac{825}{5}$$
5. **Show cancellation:**
$$x = \frac{\cancel{825}^{165 \times 5}}{\cancel{5}} = 165$$
6. **Answer:** The amount of sugar needed is $165$ grams.
This means if you use $275$ grams of flour, you should use $165$ grams of sugar to maintain the $5:3$ ratio.