Question

In an annual sales contest, Lisa sold $188, $212, $214, $196, and $200 worth of products in the first five years. In order to qualify for the grand prize, she must average at least $205 over six years. What is the least amount she must sell in the sixth year in order to qualify?

Answer 1

The answer is 220 at least. Here's how it goes
Multiply $205 with 6 and subtract the sum of the five years from it. That's how I think and I hope it helps

Answer 2

Answer: $220

Explanation:

Formula to find Average :

`\text{Average}=\frac{\text{Sum of all observations}}{\text{Total number observations}}`

Let x be the amount she must sell in the sixth year in order to qualify.

Given : In an annual sales contest, Lisa sold $188, $212, $214, $196, and $200 worth of products in the first five years.

Then, the average over six years would be

`\text{Average}=(188+212+214+196+200+x)/(6)`

In order to qualify for the grand prize, she must average at least $205 over six years.

i.e.
`\text{Average}=(188+212+214+196+200+x)/(6)\geq205`

`\Rightarrow\ (1010+x)/(6)\geq205`

`\Rightarrow\ 1010+x\geq205*6`

`\Rightarrow\ 1010+x\geq1230`

`\Rightarrow\ x\geq1230-1010`

`\Rightarrow\ x\geq220`

Hence, the least amount she must sell in the sixth year in order to qualify= $220