Question

10. Mary has received the following grades on her first 4
Math tests: 87, 93, 91 and 88. What grade must she
receive on her 5th test to have an average of 90 in the
class?
Ans.​

Answer 1

Answer:

let the Mark's obtained in her 5th test be x

since, average mark=sum of all marks/total no of test

hence, 90=87+93+91+88+x/5

:》90=359+x/5

:》90×5-359=x

:》450-359=x

:》x=91

hence, Mary got 91 Mark's in her 5th test

Answer 2

Mary must receive 91 on her 5th test to have an average of 90 in the class

Given :

Mary has received the following grades on her first 4 Math tests : 87 , 93 , 91 and 88

To find :

The number Mary must receive on her 5th test to have an average of 90 in the class

Solution :

Step 1 of 2 :

Form the equation to calculate the number Mary must receive on her 5th test

Mary has received the following grades on her first 4 Math tests : 87 , 93 , 91 and 88

Let Mary must receive x on her 5th test to have an average of 90 in the class

Number of tests = 5

Total marks in 5 tests

= 87 + 93 + 91 + 88 + x

= x + 359

We know that ,

$\displaystyle \sf{ \frac{Sum \: of \: the \: observations}{Number \: of \: observations} = Average }$

So by the given condition

$\displaystyle \sf \frac{x + 359}{5} = 90$

Step 2 of 2 :

Calculate number Mary must receive on her 5th test

$\displaystyle \sf \frac{x + 359}{5} = 90$

$\displaystyle \sf{ \implies }x + 359 = 90 \times 5$

$\displaystyle \sf{ \implies }x + 359 = 450$

$\displaystyle \sf{ \implies }x = 450 - 359$

$\displaystyle \sf{ \implies }x = 91$

Hence Mary must receive 91 on her 5th test to have an average of 90 in the class

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