Question

You scored 88, 92 and 87 on three tests. How do you write and solve an equation to find the score you need on the fourth test so that your mean test score is 90?

Answer 1

Hint: We need to understand that we are solving for the average, which we already know the average value of four test scores is 90. Since we know the values of the first three test scores, and we know what our final value needs to be. That is we need to add all the scores then divided by number of tests. That is
 \[{\text{Avarage score}} = \dfrac{{{\text{all the test scores obtained}}}}{{{\text{number of tests}}}}\] .

Complete step-by-step answer:
If we don’t count the fourth test then the average of the three tests are given by \[\dfrac{{88 + 92 + 87}}{3}\] , whatever the value it may be. We don’t need this. We need to find the score of the fourth test.
Given that the average of the four tests is 90.
Let ‘x’ be the score of the fourth test.
Then we have,
 \[ \Rightarrow \dfrac{{88 + 92 + 87 + x}}{4} = 90\]
Multiply by ‘4’ on both sides we get,
 \[ \Rightarrow 88 + 92 + 87 + x = 90 \times 4\]
Adding in the left hand side of the equation and multiplying the terms in the right hand side of the equation, we have:
 \[ \Rightarrow 267 + x = 360\]
Subtract 267 on both sides we have,
 \[ \Rightarrow x = 360 - 267\]
 \[ \Rightarrow x = 93\]
Thus the score of the fourth test is 93.
So, the correct answer is “93”.

Note: We can check whether the obtained answer is correct or not, take the average of these four test we have \[ \Rightarrow \dfrac{{88 + 92 + 87 + 93}}{4} = \dfrac{{360}}{4} = 90\] . Hence it checks out that the obtained answer is correct. Follow the same procedure for these kinds of problems. Remember the formula for average score.