Question

Solve 9/n = 75/100 for the unknown quantity, n.

Answer 1

• 
  `n = 12`

Explanation:

To find:-

• The value of "n" .

Answer:-

The given equation to us is ,

`\longrightarrow (9)/(n)=(75)/(100) \\`

Simplify the RHS of the equation. This can be done by dividing the numerator and denominator by 25 as it is the HCF of 75 and 100 . So we have;

`\longrightarrow (9)/(n)=(75/ 25)/(100/ 25) \\`

Simplify,

`\longrightarrow (9)/(n) = (3)/(4) \\`

Flip the numerator and denominator on both the sides , as ;

`\longrightarrow (n)/(9) =(4)/(3) \\`

Multiply both the sides by 9 as ,

`\longrightarrow (n)/(9)* 9 =(4)/(3)* 9\\`

Simplify,

`\longrightarrow \boxed{\boldsymbol{ n = 12}} \\`

Henceforth the value of n is 12 .

Answer 2

n = 12

Explanation:

Given equation:

`(9)/(n)=(75)/(100)`

We can solve the equation for the unknown quantity, n, by cross-multiplying, which means multiplying both sides of the equation by the product of the denominators.

The denominator of a fraction is the part below the division bar.

The denominators of the given equation are n and 100, so their product is 100n.

Multiply both sides by 100n:

`\implies (9)/(n) \cdot 100n=(75)/(100)\cdot 100n`

Simplify and cancel the common factors:

`\implies (9\cdot 100n)/(n) =(75\cdot 100n)/(100)`

`\implies 9\cdot 100 =75\cdot n`

`\implies 900 =75n`

To solve for n, divide both sides of the equation by 75:

`\implies (900)/(75) =(75n)/(75)`

`\implies 12=n`

Therefore, the unknown quantity, n, is 12.