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Teacher tells the student that the highest mark obtained by a student is $9$ more than thrice the lowest mark. If the highest score is $90$ then what is the lowest score?

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Last updated date: 25th Feb 2024
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IVSAT 2024
Answer
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Hint: In this type of question we will simply proceed according to the given statement. Here we need to find the lowest score so we will let it be a variable. Then we must know that thrice of the number means that we have to do it three times. Similarly twice of the number is two times of that number. For example: If we have the number $x$ then thrice that number will be $3x$ and twice that number will be $2x$. In this way we will convert the statement in the equation form and solve it to get the required result.

Complete step-by-step answer:
Here we are given that the highest mark obtained by a student is $9$ more than thrice the lowest mark.
So first of all we need to know what thrice of the number means. Here we must know that thrice of the number means that we have to do it three times. Similarly twice of the number is two times of that number. For example: If we have the number $x$ then thrice that number will be $3x$ and twice that number will be $2x$. In this way we will convert the statement in the equation form and solve it to get the required result.
So let the lowest marks to be found be $y$
Thrice of the lowest marks $ = 3y$
And we are told that highest mark is $9$ more than the thrice of the lowest marks which means
${\text{highest marks}} = 3y + 9$$ - - - - (1)$
Also we know that the highest mark is $90$
Putting its value in the equation (1) we get that
$90 = 3y + 9$
$\Rightarrow$ $3y = 90 - 9$
$\Rightarrow$ $3y = 81$
$\Rightarrow$ $y = 27$
So we get that the lowest marks$ = 27$

Note: Here in this type of question we must know what thrice and twice of the number means. We must have the practice of the questions where we need to convert the statement into the equation form and then we can easily solve such types of problems.
For example: If we are given that twice of the number $x$ is $40$ it means that $2x = 40$