There are green and red counters in a bag. There are 30 counters in total. The ratio of red to green counters is 1 : 5. There are 5 red counters in the bag. How many green counters are in the bag?

There are 30 counters in total in the bag. If we visualise the ratio as there being x red counters and 5x green counters, we find that there are 6x counters in total in the bag, and thus we can conclude that 6x = 30. Then we can work out x as 30/6 =5. Finally, we know that there are 5x green counters in the bag, so the number of green counters will be 5 * 5 = 25. So there are 25 green counters.
This question could be continued, for instance by stating that more of a certain colour of counters is added to the bag, then giving the new ratio and asking the student to calculate the number of counters that were added to the bag.

Answered by Jack S. Maths tutor

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