Question

QUESTION 3For Amy to get a Cin biology, her test scores must average between 70%-80%, inclusive.She has 63%,83%, and 76% on the first three tests this semester.What range of scores on the fourth test would give her a c?between 58% and 98%, inclusivebetween 63% and 93%, inclusivebetween 70% and 80%, inclusive93% or better

Answer 1

Given:

Test scores average between 70% - 80%

First, three test is 63%, 83%, 76%

Find-: Range score on the fourth test.

Sol:

Average scores = 70% - 80%

Let the fourth test score is "x" then

The average of all four tests is:

`=(63+83+76+x)/(4)`

So the average range is:

`\begin{gathered} (63+83+76+x)/(4)\ge70 \\ \\ 63+83+76+x\ge70*4 \\ \\ 222+x\ge280 \\ \\ x\ge280-222 \\ \\ x\ge58 \end{gathered}`

For average upper range,

`\begin{gathered} (63+83+76+x)/(4)\leq80 \\ \\ 222+x\leq320 \\ \\ x\leq320-222 \\ \\ x\leq98 \end{gathered}`

So fourth test score range is:

`\text{ Between }58\%\text{ and }98\%,\text{ inclusive}`