# System of Equations Problem

Alexa Tierney

Vivien is trying out cupcake flavors for her birthday, and she plans on buying a certain number of each flavor. The first flavor red velvet costs $2.00, and the second flavor chocolate peanut butter cost $1.50 If 25 people are attending her party how many cupcakes can she buy of each if her budget is $45?

X represents the amount of red velvet cupcakes bought, and the domain on the graph below.

Y represents the amount of chocolate peanut butter cupcakes and the range in the graph below.

## Work and Explanation

My two equations used to represent these problems are x+y=25 and 2.00x+1.50y=45

## Graph of My System of Equations

## Analysis of Results

My results represent the point at which you would stay in budget while buying 25 red velvet and chocolate peanut butter cupcakes. This means that event though you could change the amount of cupcakes for each flavor, you would be over or under the budget of $45. I completed and analyzed this problem because it interested me in how I could find the amount of cupcakes I could get for my birthday while setting a budget that I could stay within. These types of problems occur in real life because while planning a wedding or a party one normally has a set budget, so if one used this method they could solve a system of equations to find a way to stay within their budget.