Question 58·Easy·Linear Equations in Two Variables
A bakery sells small muffins for $1.25 each and large muffins for $2.75 each. If the bakery earns a total of $235 from selling small muffins and large muffins, which equation represents this situation?
For word problems that ask you to write an equation, first define each variable clearly. Then, for each piece of the situation, translate words into algebra using "price (or rate) × quantity" to get expressions, and decide whether to add or subtract those expressions. Finally, set the combined expression equal to the given total and match your equation to the answer choices by checking that each variable has the correct coefficient and that the operations (plus or minus) make sense.
Hints
Identify what and stand for
Ask yourself: Do and represent amounts of money or numbers of muffins? How does that affect how they appear in an equation about money?
Turn prices and quantities into expressions
To find the money from one type of muffin, what operation do you use with "price per muffin" and "number of muffins"?
Combine the parts into a total
Once you have an expression for money from small muffins and an expression for money from large muffins, should you add or subtract them to get the total? Then set that total equal to 235.
Desmos Guide
Build the total-earnings expression
In Desmos, type an expression that represents "money from small muffins plus money from large muffins" using and . For each part, use (price per muffin) * (number of muffins). For example, type something like price_small * s + price_large * l, filling in the actual prices from the problem.
Compare your expression to the answer choices
Look at the left-hand side of each answer choice and compare it to the expression you wrote in Desmos: check which coefficient goes with , which coefficient goes with , and whether there is a plus or minus sign. The choice whose left side exactly matches your expression, with the equation set equal to 235, is the correct model.
Step-by-step Explanation
Understand what the variables mean
The problem says the bakery sells small muffins and large muffins.
- is the number of small muffins sold (a count, not money).
- is the number of large muffins sold (also a count, not money).
Write the money from each type of muffin
Each small muffin costs $1.25. If small muffins are sold, the money from small muffins is:
- , which we write as .
Each large muffin costs $2.75. If large muffins are sold, the money from large muffins is:
- , which we write as .
Combine to represent the total money
The total money the bakery earns from all muffins is the sum of the money from small muffins and the money from large muffins.
So the expression for the total earnings in dollars is:
- .
Set the total equal to 235 and match the equation
The problem says this total amount of money is $235 dollars. That means we set our total earnings expression equal to 235:
This matches choice C, so is the correct equation.