Question

Brian got grades of 92, 89 and 86 on his first three math tests. What grade must he get on his final test to have an overall average of 90?
A. 90
B. 93
C. 87
D. 85

Answer 1

Hint: In this type of question where the unknown data is required then assume it to be some variable and after solving we get the required answer. This is a formula-based question so one must know the formula to solve this particular question.
Formula used:
$\text{Average} = \dfrac{{{x_1} + {x_2} + {x_3} + \cdot \cdot \cdot + {x_n}}}{n}$
Where, ${{\text{x}}_{\text{1}}}{\text{,}}{{\text{x}}_{\text{2}}}{\text{,}}{{\text{x}}_{\text{3}}}{\text{,}}...{\text{,}}{{\text{x}}_{\text{n}}}$ are the different numbers whose average is calculated and,
n=total number of data

Complete step-by-step solution:
Given,
${x_1} = 92$
${x_3} = 89$
${x_3} = 86$
${x_4} = {\text{?}}$
$n = 4$
$average = 90$
$\therefore {\text{ from the formula}}$,
$average = \dfrac{{{x_1} + {x_2} + {x_3} + \cdot \cdot \cdot + {x_n}}}{n}$
\[{\text{putting the values of }}{{\text{x}}_1},{x_2},{x_3},n{\text{ and }}\text{average}\]
$ \Rightarrow 90 = \dfrac{{92 + 89 + 86 + {x_4}}}{4}$
Multiplying both sides by 4
$90 \times 4 = 92 + 89 + 86 + {x_4}$
On simplifying further,
$360 = 267 + {x_4}$
Subtracting both sides by 267
$360 - 267 = {x_4}$
$ \Rightarrow {x_4} = 360 - 267$
$ \Rightarrow {x_4} = 93$
$\because {\text{ }}{{\text{x}}_4}{\text{ is the number for which the average is 90 }}$
$and{\text{ }}{{\text{x}}_4} = 93$,
$\therefore $ He must score 93 on his final test to get an average score of 90.
So, option (b) is correct.

Note: One must know the formula to solve this type of question. In this question, three data were given and one is unknown but in other questions this can be more or less, so choose the value of n accordingly. Do not make calculation mistakes while solving the problem then the required answer would not come. Also substitute the values of the variables carefully in the equation to avoid any mistake and if values are not substituted carefully then the required would not come. If the final result comes in decimal form then do not forget to round it up if necessary. Try to solve the question step by step.