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 [tex]\frac{x}{2}[/tex] cakes, therefore 1 big box would contain [tex]\frac{x}{2}/6=\frac{x}{12}[/tex] cakes.
Let us assume she put the other half into 14 small boxes, therefore each small box would contain [tex]\frac{x}{2}/14=\frac{x}{28}[/tex] cakes.
There were 45 cupcakes in 3 big boxes and 8 small boxes altogether. That is:[tex]3(\frac{x}{12} )+8(\frac{x}{28})=45\\ 84x+96x=15120\\180x=15120\\x=84[/tex]
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
