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

Answer:

The answer is given below

Step-by-step 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 $\frac{x}{2}$ cakes, therefore 1 big box would contain $\frac{x}{2}/6=\frac{x}{12}$ cakes.

Let us assume she put the other half into 14 small boxes, therefore each small box would contain $\frac{x}{2}/14=\frac{x}{28}$ cakes.

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

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