Question

On his first three tests, Trevor scored 86, 83, and 78. What score must he get on his fourth test to have an average (mean) of 80 for all four tests?

Answer 1

Trevor must score a 73.

Set Up

We will create an equation that has four values (three knowns, one unknown) that will divide by 4 to find the average.

Our equation will look like this:

`\displaystyle (86+83+78+x)/(4)=80`

Solve

First, combine all like terms.

`\displaystyle (247+x)/(4)=80`

Then, divide the fraction.

`\displaystyle (247)/(4) + (x)/(4) = 80`

Subtract 247/4 from both sides of the equation.

`\displaystyle (247)/(4) - (247)/(4) + (x)/(4) = 80 - (247)/(4)`

`\displaystyle (x)/(4) = (73)/(4)`

Then, multiply both sides of the equation by 4 to get rid of the denominator and isolate the variable.

`4*\displaystyle (x)/(4) = 4*(73)/(4)`

`x=73`

Final Answer

`\boxed{\bold{x=73}}`