Question

The ratio of number of red marbles to blue marbles is 5:4. If the number of blue marbles are 212, then the number red marbles are

Answer 1

❒ Let's consider the number of red marbles and blue marbles be 5x and 4x respectively.

Given that ,

• The total number of blue Marbles are 212 .

Therefore,

$\bigstar \:\: \bf \bigg\lgroup Blue Marbles = Total \:no. \:of \:blue\:Marbles \bigg\rgroup \:$

Or ,

$\star \:\: \bf {\overline{\underline {New\:Formed \:Equation \:: 4x = 212 \:}}}$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Solving \: for \: x \ \::}}$

$\qquad \longmapsto \sf{ 4x = 212}$

$\qquad \longmapsto \sf{ x =\cancel {\dfrac{212}{4}}}$

$\qquad \longmapsto \purple{\frak{\underline { x = 53}}}\:\:\bigstar$

Therefore,

• The value of x is 53

⠀⠀⠀⠀Finding no. of Red Marbles:

As , We know that

• Red Marbles = 5x

Here ,

• $\qquad \longmapsto \sf{ x = 53}$

Therefore,

• $\qquad \longmapsto \sf{ Red \:Marbles \:= 5 x }$

• $\qquad \longmapsto \sf{ Red \:Marbles \:= 5 (53) }$

• $\qquad \longmapsto \frak{\purple{\underline{ Red \:Marbles \:= 265 }}}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { The\:No.\;of\: Red\:Marbles \:are\:\bf{265\: }}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 2

Given:-

• There are 212 blue marbles.
• The number of red marbles and blue marbles are in the ratio 5 : 4.

To find:-

• The number of red marbles.

Solution:-

Let's assume that,

◍ The number of red marbles be 5f.

◍ The number of blue marbles be 4f.

As we're given with the number of blue marbles, we can write it as:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\sf{4f = 212}}}$

Now by solving this equation, we get:

$\longmapsto{ \sf{4f = 212}} \\ \\ \longmapsto{ \sf{f = \dfrac{ \cancel{212}}{ \cancel{4}} }} \\ \\ \longmapsto \underline{ \underline{ \sf \pmb{f = 53}}}$

So, on substituting this value in the expression formed for number of red marbles, i.e.,

$\: \: \: \: \: \: \: \: \: \: \Rightarrow{ \sf{5f}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Rightarrow{ \sf{5(53)}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Rightarrow \underline {\boxed{ \sf \pmb{ \red{265}}}}$

Verification:-

The simplified form of the fraction of number of red marbles by the number of blue marbles equals the ratio of their numbers. Let's take the L.H.S. value as 5 : 4 and R.H.S. value as:

$\longmapsto{ \sf{ \bigg( \dfrac{Number \: of \: {red} \: marbles}{Number \: of \: {blue} \: marbles} \bigg)}} \\ \\ \longmapsto{ \sf{ \frac{265}{212} }} \\ \\ \longmapsto{ \sf{ \frac{ \cancel{53} \times 5}{ \cancel{53} \times 4} }} \\ \\ \longmapsto{ \sf{ \frac{5}{4} = \underline{ \overline{\pmb{5 :4} }}}}$

Since L.H.S. equals R.H.S., the answer which was obtained by us is correct!

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