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Since the number of rubies is common to both ratios, try to find the LCM of the rubies factor is each ratio i.e. LCM of 6 and 8. This is 24. Hence, there must be 24 rubies in the least number of jewels. Solve the ratios to get 20 diamonds and 9 emeralds. Adding up all the jewels, you get 53.
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