Jana invited 17 friends to a dinner party at her house last Friday evening. She gave each guest a card with a number from 2 through 18, reserving number 1 for herself. When she had everyone paired off at the dinner table, she noticed that the sum of each couple’s numbers was a perfect square. What number did Joyce’s partner have?
Solve the following problems by following Polya’s Four-Step Method.
a. Frida delivers prescriptions for the local pharmacy. On Tuesday, she delivered 59 of the prescriptions already in the delivery van and then 34 of the remaining prescriptions. After picking up 10 more prescriptions at the store, she delivered 23 of those she had with her. She then picked up an additional 12 prescriptions and delivered 78 of those she had in the van. Finally, she up 3 more and then delivered the remaining 5 prescriptions. How many prescriptions did she deliver?
b. Jana invited 17 friends to a dinner party at her house last Friday evening. She gave each guest a card with a number from 2 through 18, reserving number 1 for herself. When she had everyone paired off at the dinner table, she noticed that the sum of each couple’s numbers was a perfect square. What number did Joyce’s partner have?
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