Josalyn B. answered • 03/27/20
Bachelors Degree in Math Ed with 5+ Years of Tutoring Experience
The first step is to label your variables. What the problem asks for is to find the price of drinks and popcorn, so let x = cost of drink and y = cost of popcorn.
Now to create our equations:
1. Chase spends a total of $40.50 on 9 drinks and 4 bags of popcorn.
Think about it. The total cost of $40.50 came from the fact that he bought 9 drinks and 4 bags of popcorn. So we will be multiplying the cost of drink (x) by 9 to get the total cost for the drink and the cost of the bag of popcorn (y) by 4 to get the total cost for the bags of popcorn and then adding these two together will give you the total cost overall. Therefore, we have $40.50 = 9x + 4y.
2. Oliver spends a total of $38.25 on 3 drinks and 5 bags of popcorn.
Once again, the process is the same as for number one. So we multiply 3 by x (the cost of drinks) and multiply 5 by y (the cost of a bag of popcorn) and then add the two together to get the total cost of $38.25. Therefore, we have $38.25 = 3x + 5y.
Now we have our system of equations:
40.50 = 9x + 4y
38.25 = 3x + 5y
There are several methods to solve a system of equations: graphing, substitution, and elimination. One of these methods works better than the others. Can you guess which one? The fact that we don't have just an x or just a y, means that the elimination method works best. Get the x's to cancel each other out and solve for y, and you will find the answer to the question of what the price of a bag of popcorn is.
If you need further assistance, like how the elimination method works, let me know.
