A teacher has 60 pentagons and octagons totaling 354 sides. How many of each pentagon and octagons does she have?

p + O = 60 . . . so . . . p = 60 - O

5p + 8O = 354

Substitute [ p = 60 - O ]:

5(60-O) + 8O = 354

300 - 5O + 8O = 354

300 + 3O = 354

3O = 54

O = 18

p = 60 - O = 42

Pentagons: 42
Octagons: 18

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Check:

p + O = 42 + 18 = 60

Sides on pentagons = 5 x 42 = 210

Sides on octagons = 8 x 18 = 144

Sum of sides = 210 + 144 = 354 yay!