Write an equation that represents the total of 120 muffins using the individually sold muffins and the muffins that came from boxes.

Write a second equation that represents the total money, $134.40, using $1.25 for each individual muffin and $4.40 for each box.

Solve your two equations together (using substitution or elimination) to find the number of boxes, then go back to the muffin-count equation to find $x$, the number of muffins sold individually.

In Desmos, type the two equations:

1. x + 4y = 120

2. 1.25x + 4.4y = 134.4

Here, think of $x$ as the number of individually sold muffins and $y$ as the number of boxes.

Look for the point where the two lines intersect on the graph. Click that intersection point; the coordinates will appear as $(x, y)$. The $x$-coordinate of this point is the number of muffins sold individually.

Let $x$ be the number of muffins sold individually, and let $b$ be the number of boxes of 4 muffins.

Each box has 4 muffins, so the total number of muffins is given by

This equation represents the total of 120 muffins sold.

Muffins sold individually cost $1.25 each, so they bring in $1.25x dollars.

Each box costs $4.40, so boxes bring in $4.40b dollars.

The total money is $134.40, so the money equation is

To avoid decimals, multiply every term by 100:

Now you have a system:

From the first equation,

Substitute this into the second equation:

Distribute $125$:

Combine like terms:

Subtract $15000$ from both sides:

Divide both sides by $-60$ to solve for $b$:

So 26 boxes of 4 muffins were sold.

Use the muffin-count equation $x + 4b = 120$ and plug in $b = 26$:

Compute $4(26) = 104$:

Subtract $104$ from both sides:

So, $16$ muffins were sold individually.