Question

Maria uses 3 cups of cocoa and 4 cups of refined flour to bake a chocolate cake.
Polly uses 2 cups of cocoa and 3 cups of refined flour.
Mary uses 12 cups of cocoa and 16 cups of flour.
Which of them bake their cakes in the same ratio?

Answer 1

Ratio of cocoa to refined flour for:
(i) Maria = 3:4 =$\frac{3}{4}$

(ii) Polly = 2:3 = $\frac{2}{3}$

(iii) Mary = 12:16 = $\frac{12}{16}$


Consider $\frac{3}{4}$ and $\frac{2}{3}$.
3 × 3 = 9
4 × 2 = 8
Here, 9 is not equal to 8.
So, $\frac{3}{4}$ and $\frac{2}{3}$ are not equivalent.


Consider $\frac{12}{16}$ and $\frac{2}{3}$.
12 × 3 = 36
16 × 2 = 32
Here, 36 is not equal to 32.
So, $\frac{12}{16}$ and $\frac{2}{3}$ are not equivalent.


Consider$\frac{3}{4}$ and $\frac{12}{16}$.
3 × 16 = 48
4 × 12 = 48
Here, the products are equal.
Therefore, 3:4 is equivalent to 12:16.
Maria and Mary have baked their cakes in the same ratio.