Question

Rick's average score on his first three tests in math is 80. What must he score on his next test to raise his average to 84?

Answer 1

Now, we don't know the scores for his first three tests. But we are told that the average score for the first three tests was 80.

So, let the scores of the first three tests be a, b, and c. That means

`(a+b+c)/(3)=80`

Also, let's assume the total score for his first three tests was x, This means that

`\begin{gathered} a+b+c=x \\ or \\ x=a+b+c \end{gathered}`

Comparing with the first equation it means that

`\begin{gathered} (a+b+c)/(3)=80 \\ (x)/(3)=80 \\ x=3*80 \\ x=240 \end{gathered}`

Now we are asked "What must he score on his next test to raise his average to 84?"

So this means the total tests becomes 4. Hence

`\begin{gathered} (a+b+c+d)/(4)=84 \\ (x+d)/(4)=84 \\ (240+d)/(4)=84 \\ 240+d=84*4 \\ 240+d=336 \\ d=336-240 \\ d=96 \end{gathered}`

So he must score 96 to raise his average score to 84.

Hence, the answer is 96