Factors and Multiples word problem

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

Every 12th customer at a Chicago deli gets a free soda. Every 15th customer gets a free bagel. Which is the first customer to get a free bagel and a free soda?

Sep 27th, 2015

Thank you for the opportunity to help you with your question!

In order for the customer to get a free soda n = 12k for some k and for the same customer n = 15j for some j. So, we must have 12k = 15j. But 12 = 2 * 2 * 3 and 15 = 3 *5, so we need k and k so that

2 * 2 * 3 * k  = 3 * 5 * j. Dividing both side by 3, this means we need 4k = 5j. If k = 5 and j = 4 we have 12 * k = 60 and 15 * j = 60, so on day 60, the customer gets a free bagel and a free soda.  

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 27th, 2015

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Sep 27th, 2015
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Sep 27th, 2015
Oct 18th, 2017
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