Question 49·Easy·Linear Equations in Two Variables
A copy shop charges $0.05 per black-and-white page and $0.12 per color page. If Jacob printed black-and-white pages and color pages for a total cost of $5.29, which equation models this situation?
For linear word problems that ask for an equation, first label the variables clearly, then turn each sentence into math by writing (rate) × (quantity) for each part. Add those parts to form the total, carefully matching each variable with its correct rate and making sure units are consistent (dollars with dollars, cents with cents). Finally, compare your equation structure to the choices and eliminate any that swap coefficients, ignore rates, or mix units.
Hints
Connect variables to costs
Ask yourself: What does count, and what does count? How much does one of each type of page cost?
Build cost expressions
Think about how to express the total cost of black-and-white pages using and , and the total cost of color pages using and .
Combine to make the total
Once you have expressions for the cost of each type of page, how should you combine them to represent the total cost of $5.29?
Check units and coefficients
Make sure the numbers multiplying and are in dollars (not cents) and are attached to the correct type of page.
Desmos Guide
Represent the cost expression
In Desmos, think about the total cost as “(cost per black-and-white page) × x + (cost per color page) × y,” and type that general structure using the numbers from the problem (do not include the = 5.29 yet).
Compare with answer choices
Now, for each answer choice, enter only its left-hand side (for example, 0.12x + 0.05y, x + y, etc.) as separate expressions in Desmos and compare them to the expression you built from the story. The one whose coefficients match the correct prices for each type of page is the correct model.
Step-by-step Explanation
Identify what the variables mean
From the problem:
- = number of black-and-white pages Jacob printed
- = number of color pages Jacob printed
We also know the prices:
- Each black-and-white page costs dollars.
- Each color page costs dollars.
Write an expression for each part of the total cost
To find the total cost for each type of page, multiply the number of pages by the cost per page:
- Total cost of black-and-white pages:
- Total cost of color pages:
These two expressions represent the separate parts of the total bill.
Combine the parts and match to an answer choice
Jacob’s total cost is the sum of the black-and-white cost and the color cost, and the problem says this total is $5.29. So the equation is
This matches answer choice C) .