Solve Applications of Inequalities

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NoGoodAtMath

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Marliee wants to earn an "A" in a class and needs an overall average of at least 92. Her test grades are 88, 92, 100, and 80. The average of her quizzes is 90 and counts as one test grade. The final exam count's as 2.5 test grades. What scores on the final exam would result in Marliee's overall average of 92 or greater?

According to my math book, the answer is 96 and I ended up with 95.2. Where did I go wrong? Thanks again.

88+92+100+80 +2.5x/6.5≥92

360+2.5x/6.5≥92(6.5)

360+2.5x≥598

2.5x≥238

=95.2
 
NoGoodAtMath said:
Marliee wants to earn an "A" in a class and needs an overall average of at least 92. Her test grades are 88, 92, 100, and 80. The average of her quizzes is 90 and counts as one test grade. The final exam count's as 2.5 test grades. What scores on the final exam would result in Marliee's overall average of 92 or greater?

According to my math book, the answer is 96 and I ended up with 95.2. Where did I go wrong? Thanks again.

88+92+100+80 +2.5x/6.5≥92

360+2.5x/6.5≥92(6.5)

360+2.5x≥598

2.5x≥238

=95.2
Click to expand...
You appear not to have included the quiz grades: "The average of her quizzes is 90 and counts as one test grade" but there is no "90" in your calculation.
 
NoGoodAtMath said:
Never mind, I found my mistake, thanks.
Click to expand...

Did you get the book answer of 96? I would have thought that it was the average of 3.5 tests where one test score was 90 and the other 2.5 test scores were x (the minimum test score needed so the average of the 3.5 test scores was at least 92). Or
\(\displaystyle \frac{90 + 2.5 x}{3.5}\ge92\)

Certainly 96 would work for x in the above inequality but it is not the minimum.
 
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