Question

a cupcake recipe designed to produce 28 cupcakes calls for 360 grams of flour. determine the quantity of flour that would be required to make 32 cupcakes.
the quantity of flour required is \boxed{} grams.

Explanation:

Step1: Find flour per cupcake

To find the amount of flour per cupcake, divide the total flour by the number of cupcakes. So, flour per cupcake is $\frac{360}{28}$ grams.

Step2: Calculate flour for 32 cupcakes

Multiply the flour per cupcake by 32. So, total flour = $\frac{360}{28} \times 32$. Simplify: $\frac{360\times32}{28} = \frac{11520}{28} = \frac{2880}{7} \approx 411.43$ (rounded to two decimal places) or as an improper fraction. But let's do exact calculation: $360\div28 = \frac{90}{7}$, then $\frac{90}{7} \times 32 = \frac{2880}{7} \approx 411.43$ or if we keep it as a fraction, but usually decimal is better here. Wait, maybe I made a miscalculation. Wait, 360 divided by 28: 2812=336, 360-336=24, so 12 + 24/28 = 12 + 6/7 = 90/7 ≈12.857. Then 90/7 32 = (9032)/7 = 2880/7 ≈411.43. Wait, but maybe the problem expects an exact fraction or a decimal. Let me check again. 360 grams for 28 cupcakes. So per cupcake: 360/28 = 90/7 ≈12.8571 grams. Then 32 cupcakes: 90/7 32 = 2880/7 ≈411.43 grams. So the quantity of flour required is $\frac{2880}{7}$ grams or approximately 411.43 grams.

Answer:

$\frac{2880}{7}$ (or approximately 411.43)