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I have a bag of marbles, where each marble is pink or yellow. The ratio of pink marbles to yellow marbles is 3:5.  If there are total of 72 marbles in the bag, how many are pink?

 Oct 11, 2018
 #1
avatar+3994 
+2

We have 3x+5x=72, 8x=72, x=9 marbles. Since pink is 3x, we have 3*9=27 marbles.

 Oct 11, 2018
 #2
avatar+7352 
+1

Let the number of pink marbles  =  p

Let the number of yellow marbles  =  y

 

The ratio of pink marbles to yellow marbles is 3:5 . This means...

the number of pink marbles / the number of yellow marbles  =  3 / 5

p / y  =  3 / 5

 

There are a total of 72 marbles in the bag. So...

the number of pink marbles  +  the number of yellow marbles  =  72

p + y  =  72

y  =  72 - p

 

Now we can use this value of  y  in the first equation and solve for  p .

p / (72 - p)  =  3 / 5

                                    Multiply both sides of the equation by  5 .

5p / (72 - p)  =  3

                                    Multiply both sides by  (72 - p)

5p  =  3(72 - p)

 

5p  =  216 - 3p

                                    Add  3p  to both sides.

8p  =  216

                                    Divide both sides by  8 .

p  =  27

 

the number of pink marbles  =  27

 Oct 11, 2018
 #3
avatar+4465 
+1

\(\dfrac{p}{y} = \dfrac{3}{5} \Rightarrow p=\dfrac{3}{3+5}72,~y = \dfrac{5}{3+5}72\\ p=3\cdot 9 = 27,~y = 5\cdot 9 = 45\)

Rom  Oct 11, 2018

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