Answer:
A) She must average $450 per year.
Step-by-step explanation:
Given:
Lucy earned $400 and $550 in interest the last 2 years.
To Find:
Average interest she should earn in each of the next 3 years so that her total earnings over the 5-year period are at least $2300.
Solution:
Let the average interest be x
Let us use inequality to represent the situation stated,
then after 5 years
![400 + 550 +3x \geq 2300](https://tex.z-dn.net/?f=400%20%2B%20550%20%2B3x%20%5Cgeq%202300)
solving the equation,
![950+3x \geq 2300](https://tex.z-dn.net/?f=950%2B3x%20%5Cgeq%202300)
![950+3x \geq 2300](https://tex.z-dn.net/?f=950%2B3x%20%5Cgeq%202300)
![3x \geq 2300 - 950](https://tex.z-dn.net/?f=3x%20%5Cgeq%202300%20-%20950)
![3x \geq 1350](https://tex.z-dn.net/?f=3x%20%5Cgeq%201350)
![x \geq\frac{1350}{3}](https://tex.z-dn.net/?f=x%20%5Cgeq%5Cfrac%7B1350%7D%7B3%7D)
![x \geq 450](https://tex.z-dn.net/?f=x%20%5Cgeq%20450%20)
Thus the average interest she should earn in each of the next 3 years so that her total earnings over the 5-year period are at least $2300 is $450 per year.