Context Inequality Graphically

Question

Austin and his children went into a restaurant where they sell drinks for $1.50 each and tacos for $3 each. Austin has $30 to spend and must buy at least 15 drinks and tacos altogether. Also, he must buy a maximum of 15 drinks. If x represents the number of drinks purchased and y represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution

Answer 1

First, you want to set up your equations with the information they provided.

We know that the drinks are $1.50, and the tacos are $3.00, and our guy only has $30 to spend in total. So to set that equation up, we should multiply the prices of the items by the items and set them equal to the total Austin will spend.

1.5x + 3y = 30

Now we should try to determine the number of each item by adding them together and setting them to the total number of items that Austin will buy. Since they tell you that Austin will be buying at least 15 items in total, we should set our second equation up as an inequality.

x + y >/= 15

Once you graph your equations, you should have your possible solution.