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.

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Answered by Jack S. Maths tutor

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