Question

Patricia baked some cupcakes for sale. she put half of the cupcakes equally into 6 big boxes and the other half equally into small boxes. There were 45 cupcakes in 3 big boxes and 8 small boxes altogether.

a) How many cupcakes dud Patricia bake?
b) She sold all the small boxes and collected $189. How much did she sell each small box for?​

Answer 1

The answer is given below

Explanation:

a)

Let us assume Patricia baked x number of cakes. She put half of the cupcakes (i.e x/2) equally into 6 big boxes.

6 big boxes contained
`(x)/(2)` cakes, therefore 1 big box would contain
`(x)/(2)/6=(x)/(12)` cakes.

Let us assume she put the other half into 14 small boxes, therefore each small box would contain
`(x)/(2)/14=(x)/(28)` cakes.

There were 45 cupcakes in 3 big boxes and 8 small boxes altogether. That is:
`3((x)/(12) )+8((x)/(28))=45\\ 84x+96x=15120\\180x=15120\\x=84`

Therefore Patricia baked 84 cup cakes

b)

She sold all the small boxes and collected $189, i.e she sold 14 small box for $189. Each small box = $189/14 = $13.5