Originally, Juan borrowed $10, but his mother loaned him $3 more, so he borrowed a total of $13. He sells $25 worth of lemonade in his first week. After Juan pays his mother back the $13 he borrowed, his profit is $12.

Question

If Juan’s mother forgave (or took away) his debt of –13, what equation shows the amount of money Juan will have?

Answer 1

To find the equation that shows the amount of money Juan will have if his mother forgives his debt, we first need to clarify a few amounts:

1. Total Revenue from selling lemonade: $25
2. Amount Juan borrowed (debt): $13 (which includes the $10 he originally borrowed and the additional $3 from his mother)
3. Profit after paying back his mother: $12

To calculate the amount of money Juan will have if his mother forgives his debt of $13, we consider the total earnings and the effect of the debt forgiveness.

If his mother forgives the $13 debt, then we can represent the amount of money Juan has as follows:

Let \( M \) be the amount Juan has:

• Initially, Juan has $25 from selling lemonade.
• With the forgiveness of the debt, we add back the $13 Juan owed.

Thus, we can write the equation for the amount of money Juan has after debt forgiveness as:

\[ M = 25 + 13 \]

This simplifies to:

\[ M = 38 \]

So the equation representing the amount of money Juan will have if his mother forgives his debt of $13 is:

\[ M = 25 + (-13) + 13 \]

This simplifies to \( M = 25 \) if you consider the debt to be forgiven, as it has no impact on his total wealth anymore. However, if counting the previously owed amount, it can be reaffirmed as:

\[ M = 25 + 13 = 38 \]

This means Juan effectively has $38 if the debt is forgiven.