Question

Will medal!! A student 98 and 87 on his first two quizzes. Use a compound inequality to find the possible value for the third quize that would give him a average between 90 and 95.
A.87= 12 years ago

Answer 1

The question can be written as
\[90 \leq \frac{98+87+x}3 \leq 95\]
which means
\[\frac{98+87+x_{low}}3 = 90\]
\[\frac{98+87+x_{high}}3 = 95\]
if we define \(x_{low}\) and \( x_{high}\) by how the numbers in the answer
\[x_{low} \leq x \leq x_{high}\]

Answer 2

So B...

Answer 3

No

Answer 4

If you choose B
\[\frac{98+87+95}3 = 93\frac13\]
\[\frac{98+87+90}3 = 91\frac23\]
The student will average between 91.6666 and 93.3333, but the question wants the student to average between 90 and 95

Answer 5

So he would have to get higher than 95 on at least one test?

Answer 6

His average on the first two tests is
\[\frac{98+87}2 = 92.5\]
So to raise the average to 95, the third test score would have to be above 95
To lower the average to 90, the third test score would have to be below 90

You can work out the two limits of test scores by solving for \(x_{low}\) and \(x_{high}\) in my first reply

Answer 7

So the solution is 87=<x=<98

Answer 8

No
\[\frac{98+87+98}3 = 94.3333...\]
\[\frac{98+87+87}3 = 90.6666...\]

Answer 9

Why not just solve the equations?
\[\frac{98+87+x_{low}}3 = 90\]
\[98+87+x_{low} = 3\times90\]
\[x_{low} = 3\times90 - 98 - 87\]
similarly
\[x_{high} = 3\times95 - 98 - 87\]

Answer 10

I don't know how to solve using xhigh and xlow

Answer 11

They're just numbers. They're nothing special.
I wrote them because the answer defines the third test score to be x, and you want to find the higher and lower limits of x.
I could write
\[x_{low} = \text{lower limit of third test score}\]
\[x_{high} = \text{higher limit of third test score}\]
so the question would be
\[\frac{98+87+\text{lower limit of third test score}}3 = 90\]
\[\frac{98+87+\text{higher limit of third test score}}3 = 95\]

Answer 12

I working on solving, So far I have xhigg=100. Is that correct.

Answer 13

\[\frac{98+87+100}3 = 95\]
Yes

Answer 14

So xlow=85 and xhigh=100. Correct?

Answer 15

\[\frac{98+87+85}3 = 90\]
Yeah, that's right :)

Answer 16

THANK YOU SO MUCH!!!! This is a real life saver!!