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a pizzeria sells three sizes of pizza: small, medium, and large. the pizzas sell for $9, $10, and $13, respectively.
one evening they sold 21 pizzas and received $220. if they sold 1 more medium than large pizzas, how many of each size did they sell?
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Let S = # small pizza; L = # large pizza.
Then you have these two equations:
S + (L +1) + L = 21, (1)
9S + L(10+13) + 10 = 220. (2)
Simplify and write in the standard form:
S + 2L = 20, (1')
9S + 23L = 210. (2')
From (1'), express S = 20 - 2L and substitute it into (2) replacing S:
9*(20-2L) + 23L = 210,
180 - 18L + 23L = 210,
5L = 210 - 180,
5L = 30 ---> L = 6.
Answer. 6 large pizzas; 7 medium pizzas and (21-6-7) = 8 small pizzas.