Question
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.
If Juan’s mother forgave (or took away) his debt of –13, what equation shows the amount of money Juan will have?
If Juan’s mother forgave (or took away) his debt of –13, what equation shows the amount of money Juan will have?
Answers
GPT-4o mini
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.
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.