Question

5) Polly wants her math average to be more than an 85. Her current grades are 70, 85, 90 and 88. Whatis the minimum grade Polly must receive in order to achieve an average of greater than an 85?Let x =Inequality:

Answer 1

The Solution:

Given Polly's grades as:

`70,85,90,88`

Let the minimum grade she needs to average more than 85 be represented with x.

By formula,

`\text{ Average grade =}\frac{\text{ sum of grades}}{\text{ number of grades}}`

In this case,

`\begin{gathered} \text{average grade =85} \\ \text{ sum of grades = 70+85+90+88+x} \\ \text{ number of grades = 5} \end{gathered}`

Substituting, we get the inequality that describes the situation as below:

`\text{ 85 }\leq(70+85+90+88+x)/(5)`

The above inequality is the same as

`(70+85+90+88+x)/(5)\ge85`

Solving the above inequality, we multiply both sides by 5.

`\begin{gathered} (70+85+90+88+x)/(5)*5\ge(85*5) \\ \\ 70+85+90+88+x\ge425 \end{gathered}`
`333+x\ge425`

Collecting the like terms, we get

`\begin{gathered} x\ge425-333 \\ \\ x\ge92 \end{gathered}`

Thus, the minimum grade Polly needs is 92.

Therefore, the correct answer is 92.