where \( c \) is the longest side:


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A museum curator is cataloging a collection of historical telescopes. She notes that the number of refracting telescopes is 3 more than twice the number of reflecting telescopes. If there are 11 reflecting telescopes, how many total telescopes are in the collection?
Let the number of reflecting telescopes be $ r = 11 $.
The number of refracting telescopes is $ 2r + 3 = 2(11) + 3 = 25 $.
Total telescopes = $ r + (2r + 3) = 11 + 25 = 36 $.
A science journalist is analyzing data from a study on bird migration patterns. The study shows that the number of birds migrating south is 4 times the number migrating north, minus 12. If 32 birds migrate south, how many migrate north?
Let the number migrating north be $ x $.