Question 137·Medium·Linear Equations in Two Variables
A print shop sells ink cartridges for dollars each and packs of paper for dollars each. The equation above represents the total amount paid, in dollars, for purchasing 3 ink cartridges and 4 packs of paper. Which of the following is the best interpretation of 116 in this context?
For word problems that give an equation, first translate each symbol into words: identify what each variable stands for, then interpret coefficients as counts (like “3 cartridges” or “4 packs”), and combine them to see what the whole expression means. Finally, look at the number on the other side of the equation and match it to that same real-world quantity, choosing the answer option that describes it most precisely.
Hints
Focus on the meaning of x and y
What does represent in the story? What does represent? Make sure you can say in words what each variable stands for.
Interpret the expression 3x + 4y
Think about what 3 times the price of one ink cartridge means, and what 4 times the price of one pack of paper means. What do you get when you add those two amounts?
Connect the equation to the constant 116
If the left side of the equation is the total cost of the items purchased, then what does the number that it equals have to represent in the real-world situation?
Desmos Guide
Enter the cost expression
Type 3x + 4y into Desmos. This expression represents the combined cost of some number of ink cartridges and packs of paper, based on their individual prices and .
Add the equation with 116
Now type 3x + 4y = 116. Notice that 116 is the number that the total cost expression is set equal to.
Interpret the constant in context
Ask yourself: if 3x + 4y stands for the cost of buying 3 cartridges and 4 packs, then what real-world quantity must the constant on the right side, 116, represent in the story?
Step-by-step Explanation
Identify what the variables represent
From the problem, is the price of one ink cartridge in dollars, and is the price of one pack of paper in dollars.
Interpret each term in the expression
The term means the cost of 3 ink cartridges (because each cartridge costs dollars).
The term means the cost of 4 packs of paper (because each pack costs dollars).
Interpret the left side of the equation
Adding these together, is the total cost of buying 3 ink cartridges and 4 packs of paper.
Match that total to the number 116
The equation says , so the number 116 represents the total amount, in dollars, paid for 3 ink cartridges and 4 packs of paper, which corresponds to choice C.