Question

Jacqui has grades of 79 and 73 on her first two algebra tests. If she wants an average of at least 79, what possible scores can she make on her third test?A. Less than 85B. Greater than 85C. 85 or lessD. 85 or greater

Answer 1

Average

D

Step-by-step explanation

There are three tests. The average is given by their sum and division by 3:

`\frac{79+73+\text{??}}{3}`

We want it to be 79 or more:

`\frac{79+73+\text{??}}{3}\ge79`

We want to find the value of the last test, ??, so the average is at least 79:

`\begin{gathered} \frac{79+73+\text{??}}{3}\ge79 \\ \downarrow\text{ since 79+73=152} \\ \frac{152+\text{??}}{3}\ge79 \end{gathered}`

`\begin{gathered} \downarrow\text{ taking 3 to the right side} \\ \frac{152+\text{??}}{3}\cdot3\ge79\cdot3 \\ 152+??\ge237 \end{gathered}`
`\begin{gathered} \downarrow\text{ taking 152 to the right} \\ -152+152+??\ge-152+237 \\ ??\ge85 \end{gathered}`

?? ≥ 85 means that the third score must be 85 or greater.

That is why the answer is D.