After the journalism club sold 60 magazines, it had [tex]$220[/tex] in profit. After it sold a total of 100 magazines, it had a total of [tex]$420[/tex] in profit. Which equation models the total profit, [tex]y[/tex], based on the number of magazines sold, [tex]x[/tex]?

A. [tex]y + 220 = 2(x + 60)[/tex]
B. [tex]y - 220 = 2(x - 60)[/tex]
C. [tex]y + 220 = 5(x + 60)[/tex]
D. [tex]y - 220 = 5(x - 60)[/tex]

To find the equation that models the total profit, [tex]$ y $[/tex], based on the number of magazines sold, [tex]$ x $[/tex], let's follow these steps:

1. Identify known points:
- When 60 magazines are sold, the profit is [tex]$220. This gives us the point $(60, 220)$.
- When 100 magazines are sold, the profit is $[/tex]420. This gives us the point [tex]$(100, 420)$[/tex].

2. Calculate the rate of profit per magazine:
- The change in profit between these two sales points is [tex]$ 420 - 220 = 200 $[/tex] dollars.
- The change in the number of magazines sold is [tex]$ 100 - 60 = 40 $[/tex] magazines.
- Hence, the profit per magazine is calculated as:
[tex]\[
\text{Profit per magazine} = \frac{200}{40} = 5 \text{ dollars per magazine}
\][/tex]

3. Determine the linear equation:
- Using the point [tex]$(60, 220)$[/tex] and the profit rate of [tex]$5$[/tex] dollars per magazine, we can find the y-intercept [tex]$b$[/tex] in the equation [tex]$ y = 5x + b $[/tex].
- Plug in the point [tex]$(60, 220)$[/tex] to find [tex]$b$[/tex]:
[tex]\[
220 = 5(60) + b
\][/tex]
[tex]\[
220 = 300 + b
\][/tex]
[tex]\[
b = 220 - 300 = -80
\][/tex]

4. Write the equation:
- The equation that models the profit based on the number of magazines sold is:
[tex]\[
y = 5x - 80
\][/tex]

5. Match with given options:
- Rearrange the equation in standard form:
[tex]\[
y - 220 = 5(x - 60)
\][/tex]
- This matches option D:
[tex]\[
\text{D. } y - 220 = 5(x - 60)
\][/tex]

So, the correct equation that models the profit is option D: [tex]$y - 220 = 5(x - 60)$[/tex].