What is the ratio of green marbles to orange marbles?

Question

A bag contains green, yellow, and orange marbles. The ratio of green marbles to yellow marbles is 2:5. The ratio of yellow marbles to orange marbles is 3:4. What is the ratio of green marbles to orange marbles?

Answer 1

Alright, Marcus.  I hope I'm not too late to help.

 

Green to yellow is 2:5 and yellow to orange is 3:4.  Remember that we always reduce ratios to their lowest terms.  Since yellow is both 5 and 3, then it has to be 15.  Make sense?

 

If yellow is 15, then we set 2/5 = x/15, letting x = green.  5x = 30, so x = 6.  

 

Again, with yellow being 15, then we set 3/4 = 15/x, letting x = orange.  3x = 60, so x = 20.

 

Then, the ratio of green to orange is 6:20 = 3:10.

 

Hope this helps!

Answer 2

The ratio of green to yellow marbles is 2/5.  That means that there is 2/5 of green marble for each yellow one.

 

Hence if the ratio of yellow to orange marbles is 3 yellow/4 orange, we can convert the yellow to green by multiplying by 2/5:

 

3 yellow        (3 yellow)*(2 green)            6 green              3 green

-------------- = ------------------------------  =  -----------------  =  ---------------

4 orange      (4 orange)*(5 yellow)         20 orange          10 orange

 

The ratio of green to orange is 3/10.