Question 1062361
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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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<pre>
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.
</pre>

<U>Answer</U>. 6 large pizzas;  7 medium pizzas and (21-6-7) = 8 small pizzas.