Vani and her children went into a bakery where they sell cupcakes for $4 each and cookies for $1.25 each. Vani has $45 to spend and must buy at least 14 cupcakes and cookies altogether. Also, she must buy a minimum of 4 cupcakes and no less than 12 cookies. If xx represents the number of cupcakes purchased and yy represents the number of cookies purchased, write and solve a system of inequalities graphically and determine one possible solution.
Let's first define our variables:
xx: the number of cupcakes purchased
yy: the number of cookies purchased
Now let's set up the inequalities:
The price of each cupcake is $4, so the cost of the cupcakes is 4xx.
The price of each cookie is $1.25, so the cost of the cookies is 1.25yy.
We have a total of $45 to spend, so the cost of the cupcakes and cookies must be less than or equal to $45:
4xx + 1.25yy ≤ 45
We must buy at least 14 cupcakes and cookies altogether:
xx + yy ≥ 14
We must buy a minimum of 4 cupcakes:
xx ≥ 4
We must buy no less than 12 cookies:
yy ≥ 12
Now let's graph these inequalities on a coordinate plane and determine a possible solution.