To determine how much money Juan will have left after paying back his mother, we need to go through the information step by step.
- Juan borrowed a total of $13 ($10 from one source and $3 from his mother).
- He sells $25 worth of lemonade in his first week.
- After selling lemonade, Juan has $25.
- He needs to pay back his mother the $3 she loaned him.
Now we will calculate how much money he has left after the repayment:
- Total money after sales: $25
- Amount to pay back to his mother: $3
Remaining money after paying his mother:
\[ $25 - $3 = $22 \]
However, the question asks for how much money he will have left after paying back just his mother, not the total after all expenses. Since the question focuses on the repayment to his mother, and it seems it may have been misunderstood in context.
If his total remains, after repayment, is considered, it will be $22 as calculated already, but if we only need to count the answer options reflected and if we disregard the amount paid back, he could retain $25 before repayment.
The answer options do not match correctly with the calculation since the question wording specifies remaining after repayment to his mother only.
Out of the provided options, the correct approach was to determine the net left ($22), but if we look at the liquidity before any repayment it conveys a broader calculation.
Thus, strictly from the selections provided:
- $25 - value left untouched before any repayment.
- $10, $12, $13 are not valid after correct accounting of the original calculation.
Assuming return is accounted primarily on the $3 to his mother, Juan maintains $22 in total after all said dealings and thus the inferred value remains $25 before his $3 interacted.
So his final monetary state after calculations stands as $22 before interaction, confirmed not by initial conditions but reflects the runtime events from sales made above all such considerations.
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