SOLUTION: An art dealer sold 12 photographs for $455. He sold some of them at $35 and the rest at $40 each. How many photographs did he sell at each price?

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Question 396093: An art dealer sold 12 photographs for $455. He sold some of them at $35 and the rest at $40 each. How many photographs did he sell at each price?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of photos sold @ $35 each
Let b = number of photos sold @ $40 each
given:
(1) 35a+%2B+40b+=+455
(2) a+%2B+b+=+12
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Divide both sides of (1) by 5
(1) 7a+%2B+8b+=+91
Multiply both sides of (2) by 7
and subtract (2) from (1)
(1) 7a+%2B+8b+=+91
(2) -7a+-+7b+=+84
b+=+7
And, from (2),
a+%2B+7+=+12
a+=+5
5 photos were sold @ $35 each
7 photos were sold @ $40 each