SOLUTION: plain pizza cost $7 each and a deluxe pizza costs $9 each. to feed the cast and crew of a high school production, the school ordered 30 pizzas in total and spent $250. How many of

Question 1202500: plain pizza cost $7 each and a deluxe pizza costs $9 each. to feed the cast and crew of a high school production, the school ordered 30 pizzas in total and spent $250. How many of each type of pizza were ordered?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52910)   (Show Source): You can put this solution on YOUR website!
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plain pizza cost $7 each and a deluxe pizza costs $9 each.
to feed the cast and crew of a high school production, the school ordered 30 pizzas
in total and spent $250. How many of each type of pizza were ordered?
~~~~~~~~~~~~~~~~~~~~~

Let n be the number of the $9 pizzas. Then the number of the $7 pizzas is (30-n). Write the total money equation 9n + 7(30-x) = 250 dollars. Simplify and find n 9n + 210 - 7n = 250 9n - 7n = 250 - 210 2n = 40 n = 40/2 = 20. ANSWER. 20 pizzas at $9 each and 30-20 = 10 pizzas at $7 each. CHECK. 20*9 + 10*7 = 180 + 70 = 250 dollars total. ! correct !

Solved.

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!

The other tutor showed a good typical formal algebraic solution, which is likely what was wanted.

But note that you can get some good mental exercise, and good problem-solving experience, by solving the problem using logical reasoning and simple mental arithmetic.

Here is one way you might solve this problem informally.

If all 30 pizzas were plain, the total cost would have been 30($7) = $210.
The actual total cost was $250, which is $40 more than $210.
The "extra" cost of each deluxe pizza is $9-$7 = $2.
The number of deluxe pizzas needed to make that additional $40 of cost is $40/$2 = 20.

ANSWER: 20 deluxe pizzas; and 30-20 = 10 plain pizzas.

CHECK: 20($9)+10($7) = $180+$70 = $250

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!

PRICES QUANTITY COST
7 30-d 7(30-d)
9 d 9d
TOTAL 30 250

d, how many deluxe pizzas

.
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