Question

I half dozen cupcakes cost $15. What constant of proportionality relates to the numbers of cupcakes and the total cost? Write an equation that represents its relationship

Answer 1

The constant of proportionality is 2.5 dollar per cupcake and then the required equation would be
`y=2.5x`.

Explanation:

Given:

Let the number of cupcakes be represent by
`'x'`

Also let the total cost be represented by
`'y'.`

We know that two proportional quantities are in for;

`y=kx`

where, k⇒ represents constant of proportionality.

Now we know that;

1 dozen = 12

Half dozen = 6

Now Given:

half dozen cupcakes cost $15.

So Let us substitute
`x=6` and
`y=15` in above equation we get;

`15 =k * 6`

Dividing both side by 6 we get;

`(15)/(6)=(k6)/(6)\\\\k= 2.5 \ \$/cupcake`

Hence the constant of proportionality is 2.5 dollar per cupcake and then the required equation would be
`y=2.5x`.