Question 52·Easy·Linear Equations in Two Variables
A coffee shop sells its house‐blend beans in two bag sizes. A small bag contains 12 ounces of beans, and a large bag contains 20 ounces of beans. On a certain day, the shop sold a total of 4,400 ounces of house‐blend beans.
Which equation models this relationship, where is the number of small bags sold and is the number of large bags sold?
For equation-modeling questions, start by clearly labeling each variable, then write an expression for the quantity the problem is tracking (here, total ounces) by multiplying each variable by its per-unit amount and adding. Finally, set this expression equal to the given total and check that your equation uses the correct units and reasonable-sized numbers—this quickly rules out options with swapped coefficients, unnecessary decimals, or incorrect totals.
Hints
Connect each variable to ounces
Ask yourself: How many ounces come from all the small bags together? How many ounces come from all the large bags together?
Build the total with addition
Once you know the ounces from small bags and from large bags, how do you combine them to get the total amount sold that day?
Match the units and the size of the numbers
The total is 4,400 ounces. Which options keep the coefficients in ounces (not tiny decimals) and use a total that makes sense compared to 4,400?
Desmos Guide
Represent the total ounces expression
In Desmos, create sliders for and . Then type the expression 12x + 20y to represent the total ounces from small (12-ounce) bags and large (20-ounce) bags.
Connect to the problem’s total
Notice that this expression gives the total ounces sold for any combination of and . The problem says the total must be 4,400 ounces, so think about setting this expression equal to 4,400, and then choose the option whose equation does exactly that, without swapping 12 and 20 or changing them to tiny decimals.
Step-by-step Explanation
Identify what the variables represent
The problem tells you that:
- is the number of small bags sold.
- is the number of large bags sold.
A small bag has 12 ounces, and a large bag has 20 ounces.
Write an expression for the total ounces sold
Each small bag contributes 12 ounces, and there are small bags, so small bags contribute ounces.
Each large bag contributes 20 ounces, and there are large bags, so large bags contribute ounces.
So, the total ounces sold can be written as:
Set the total equal to 4,400 ounces
The problem says the shop sold 4,400 ounces of beans that day. That means the total ounces expression must equal 4,400:
This matches choice D.