Maria and Luis bought notebooks and folders at the same store. Each notebook cost the same amount, and each folder cost the same amount.
- Maria bought 2 notebooks and 3 folders for a total of $19.
- Luis bought 5 notebooks and 2 folders for a total of $31.
Which choice represents this situation, where is the price, in dollars, of one notebook and is the price, in dollars, of one folder?
For a word problem asking for a system of equations, first identify what each variable represents. Then write one equation for each person by multiplying each item count by its price and setting the sum equal to that person’s total. Finally, choose the option containing both equations; solving the system is unnecessary unless you want to verify it.
Hints
Focus on what x and y represent
The problem defines and for you. Think about how you would write the total cost of some notebooks and folders using and .
Turn Maria’s description into an equation
Maria buys 2 notebooks and 3 folders for 19 dollars. Using the form (number of notebooks) + (number of folders) = total, what does her equation look like?
Turn Luis’s description into an equation
Do the same for Luis: he buys 5 notebooks and 2 folders for 31 dollars. Once you have both equations, look for the answer choice that contains both of them together.
Desmos Guide
Translate the purchases first
Desmos is not needed to choose the system because this is a direct translation problem. Write one equation for Maria’s purchase and one for Luis’s purchase, then match both equations to a choice.
Verify the selected system in Desmos
For a quick check, enter and on separate lines in Desmos. Click their intersection point to see the notebook and folder prices that satisfy both equations.
Check both totals
Use the intersection coordinates in Maria’s and Luis’s totals. Confirm that equals and that equals .
Step-by-step Explanation
Define the variables and the equation pattern
The problem tells you that is the price of one notebook and is the price of one folder. Any total cost will be:
We will use this pattern for Maria and for Luis.
Write the equation for Maria’s purchase
Maria bought 2 notebooks and 3 folders for a total of 19 dollars.
Using the pattern:
- Number of notebooks: 2, so the notebook term is .
- Number of folders: 3, so the folder term is .
- Total cost: 19.
So Maria’s equation is:
Write the equation for Luis’s purchase
Luis bought 5 notebooks and 2 folders for a total of 31 dollars.
Using the same pattern:
- Number of notebooks: 5, so the notebook term is .
- Number of folders: 2, so the folder term is .
- Total cost: 31.
So Luis’s equation is:
Match both equations to the answer choices
We now know the system that represents the situation must be
Looking at the options, this pair appears in choice C as , , so choice C is the correct answer.