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?

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

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JeanaShupp JeanaShupp · Answer 2 · 2019-11-18T04:20:42+01:00

Answer: $220

Step-by-step explanation:

Formula to find Average :

[tex]\text{Average}=\dfrac{\text{Sum of all observations}}{\text{Total number observations}}[/tex]

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

[tex]\text{Average}=\dfrac{188+212+214+196+200+x}{6}[/tex]

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

i.e. [tex]\text{Average}=\dfrac{188+212+214+196+200+x}{6}\geq205[/tex]

[tex]\Rightarrow\ \dfrac{1010+x}{6}\geq205[/tex]

[tex]\Rightarrow\ 1010+x\geq205\times6[/tex]

[tex]\Rightarrow\ 1010+x\geq1230[/tex]

[tex]\Rightarrow\ x\geq1230-1010[/tex]

[tex]\Rightarrow\ x\geq220[/tex]

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