Question

a baker in 70 minutes iced 40 cupcakes and in 49 minutes iced 28 cupcakes what is the constant of proportionaltiy

Answer 1

Constant of proportionality k = 7/4 if we take the proportionality relationship as ... number of minutes ∝ number of cupcakes Bor

number of minutes = k . (number of cupcakes)

Explanation:

If a variable x is directly proportional to another variable y indicated by
x ∝ y

Then x = k.y where k is the constant of proportionality

Letting x be the number of cupcakes and y the number of minutes

number of cupcakes = k . (number of minutes)
k = (number of minutes) / (number of cupcakes )
Here k, the constant of proportionality tells you how many many minutes it takes to ice 1 cupcake

For 40 cupcakes it takes 70 minutes. So k = 70/40 = 7/4

For 28 cupcakes it takes 49 minutes so for 1 cupcake it takes 49/28 = 7/4 so again that is the constant of proportionality

k = 7/4 given that number of minutes ∝ number of cupcakes

=> number of minutes = k. number of cupcakes

Note if we had x = number of cupcakes and y = number of minutes then k = 4/7 which is the number of cupcakes that can be iced in 1 minute

So one has to be careful to state what is proportional to what