Final answer:
The equation that shows the amount of money Juan will have after his mother forgives his debt is x = $26.
Step-by-step explanation:
To find the amount of money Juan will have after his mother forgives his debt, we can set up an equation. Let x represent the amount of money Juan will have.
Initially, Juan borrowed $10 and his mother loaned him $3 more, so he had a total of $13.
After selling $25 worth of lemonade, his profit is $12. Therefore, the equation is: 13 + 25 - x = 12.
Simplifying the equation, we have: 38 - x = 12. Rearranging the equation, we get: x = 38 - 12.
Calculating, x = 26.
So, the equation that shows the amount of money Juan will have after his mother forgives his debt is x = $26.