Question

In a certain class, the ratio of passing students to failing students is 7: 5. If there are 36 students, how many students failed the course

Answer 1

Answer :-

$\: \: \\ \large{\underline{\underline{\sf{\leadsto \: \: Firstly, \: let's \: understand \: the \: concept \: used \: :-}}}}$

Here the concept of Ratios of two numbers has been used. We see we are given with ratio of two numbers. That means there will be a number x which is variable by which both the numbers should be multiplied to get the original value.

Let's do it !!

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★ Formula Used :-

$\: \\ \large{\boxed{\boxed{\sf{7x \: \; + \: \; 5x \: \: = \; \; \bf{36}}}}}$

$\: \\ \large{\boxed{\boxed{\sf{Number \: of \: Students_{(passed\: or \: failed)} \: = \: \bf{Ratio \: part \: \times \: Value \: of \: x}}}}}$

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★ Question :-

In a certain class, the ratio of passing students to failing students is 7: 5. If there are 36 students, how many students failed the course.

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★ Solution :-

Given,

» Ratio of passing students to failing students = 7 : 5

» Total number of students = 36

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~ For the value of x :-

$\: \\ \qquad \large{\sf{:\Longrightarrow \: \: \: (Number\:of\:Passed\:students) \: \; + \: \; (Number\:of\:failed\:students) \: \: = \; \; \bf{36}}}$

$\: \\ \qquad \large{\sf{:\Longrightarrow \: \: \: 7x \: \; + \: \; 5x \: \: = \; \; \bf{36}}}$

$\: \\ \qquad \large{\sf{:\Longrightarrow \: \: \: 12x \: \; \: \: = \; \; \bf{36}}}$

$\: \\ \qquad \large{\sf{:\Longrightarrow \: \: \: x \: \; \: \: = \; \; \bf{\dfrac{\cancel{36}}{\cancel{12}} \: \: = \: \: \underline{\underline{3}}}}}$

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~ For the number of each students :-

$\: \\ \large{\sf{\rightarrow \: \: \: Number \: of \: Students_{(passed\: or \: failed)} \: = \: \bf{Ratio \: part \: \times \: Value \: of \: x}}}$

$\: \\ \qquad \large{\sf{\longrightarrow \: \: \: Number \: of \: Students \: Passed\: = \: \bf{7 \: \times \: 3 \: \: = \: \: \underline{\underline{21}}}}}$

$\: \\ \qquad \large{\sf{\longrightarrow \: \: \: Number \: of \: Students \: Failed \: = \: \bf{5 \: \times \: 3 \: \: = \: \: \underline{\underline{15}}}}}$

$\: \\ \large{\underline{\underline{\rm{\leadsto \: \: \: Thus, \; the \; number \; of \; students \; who \; failed \; in \; course \; are \;\; \boxed{\bf{15}}}}}}$

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$\: \\ \large{\underline{\sf{\leadsto \: \: \: Confused? \; Don't \; worry\; let's \; verify\; it \; :-}}}$

For verification, we need to simply apply the value we got into the equation we formed, then :-

$\: \\ \sf{\rightarrow \: \: \: 7x \: \; + \: \; 5x \: \: = \; \; 36}$

$\: \\ \sf{\rightarrow \: \: \: 7(3) \: \; + \: \; 5(3)\: \: = \; \; 36}$

$\: \\ \sf{\rightarrow \: \: \: 21 \: \: + \: \: 15 \: \: = \; \; 36}$

$\: \\ \bf{\rightarrow \: \: \: 36 \: \: = \; \; 36}$

Clearly, LHS = RHS. Here the condition satisfies. So our answer is correct.

Hence, Verified.

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$\: \\ \large{\underbrace{\underbrace{\sf{More \;\: to \;\: know \;\: :-}}}}$

• Polynomials are the mathematical expressions which are formed using constant and variable terms. But the variable terms are of single degrees. They are :-

• Linear Polynomial
• Quadratic Polynomial
• Cubic Polynomial
• Bi - Quadratic Polynomial

• Linear Equations are the equations formed using constant and variable terms and these variable terms are of single degree that is 1 .

They are :-

• Linear Equation in One Variable
• Linear Equation in Two Variable
• Linear Equation in Three Variable

The one which we solved now is the method of Linear Equation in One Variable.

• Methods to solve Linear Equation in Two Variable :-

• Substitution Method
• Cross Multiplication Method
• Elimination Method
• Reducing the pair method.

Answer 2

Given,

In a certain class, the ratio of passing students to failing students is 7: 5. There are 36 students.

To find :

How many students failed the course .

Solution :

Let the number of passing students be 7m and number of failing students be 5m.

Now atq,

⇒ 7m + 5m = 36

⇒ 12m = 36

⇒ m = 36/12

⇒ m = 3

Now,

Number of passing students = 7m = 7(3) = 21

Number of failing students = 5m = 5(3) = 15

Therefore,

15 students failed in the course.