Answer: We need to support her work for at least 15 days.
Explanation:
Juana's mother receives a daily payment of 30 soles .
She has already 120 soles.
Let x = Number of days to save at least 550 soles.
Then, Total she has after x days = 120+30x
According to the question, we have
![120+30x \geq 550\\\\\Rightarrow\ 30x\geq550-120\\\\\Rightarrow\ 30x\geq430\\\\\Rightarrow\ x\geq(430)/(30)\\\\\Rightarrow\ x\geq14.33](https://img.qammunity.org/2021/formulas/mathematics/college/66f0oqzl9fnp4353fkd5wdqm3xerxw8r31.png)
i.e. minimum value for x=15
Hence, we need to support her work for at least 15 days.