Question 43·Easy·Linear Equations in Two Variables
At a bake sale, brownies were sold for $6 each and cookies were sold for $2 each, raising a total of $120. If represents the number of brownies sold and represents the number of cookies sold, which equation best models this situation?
For equation-modeling word problems, first identify what each variable stands for and what quantity the problem is tracking (here, total money). Write a separate term for each item as (price per item) × (number of items), add those terms to represent the total, and then set this sum equal to the given total amount. Finally, match your equation to the answer choices without spending time solving for the variables unless the question specifically asks for their values.
Hints
Focus on what and mean
and are counts of items, not amounts of money. Think about how to turn those counts into dollars.
Use price × quantity
How do you calculate the money from selling brownies at $6 each? How about from selling cookies at $2 each?
Relate the expressions to the total
Once you have expressions for the money from brownies and cookies, how can you combine them and use the fact that the total raised was $120?
Desmos Guide
Represent each type of item as an expression
In one Desmos line, type 6*b to represent the money from brownies. In another line, type 2*c to represent the money from cookies.
Form the total money expression
On a new line, type 6*b + 2*c. This expression shows the total money raised in terms of and .
Match the expression to an equation choice
Look at the left-hand side of each answer choice and see which one has the same structure as the total-money expression from Desmos, and then use the fact that the total money is $120 to decide which equation matches the situation.
Step-by-step Explanation
Identify what the variables represent
We are told that is the number of brownies sold and is the number of cookies sold. The equation must connect and to the total money raised.
Write expressions for money from each item
Each brownie costs $6, so selling brownies brings in dollars. Each cookie costs $2, so selling cookies brings in dollars.
Combine the parts and match the total
The total money raised is the sum of the money from brownies and cookies: . This total equals the $120 raised, so the correct equation is , which corresponds to choice C.