SOLUTION: An art dealer sold 16 etchings for $630. He sold some of them at $35 each and the rest at $45 each. How many etchings did he sell at each price?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An art dealer sold 16 etchings for $630. He sold some of them at $35 each and the rest at $45 each. How many etchings did he sell at each price?      Log On


   



Question 445448: An art dealer sold 16 etchings for $630. He sold some of them at $35 each and the rest at $45 each. How many etchings 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 sold @ $35 each
Let b = number sold @ $45 each
given:
(1) +a+%2B+b+=+16+
(2) +35a+%2B+45b+=+630+
---------------------
Multiply both sides of (1) by 35
and subtract (1) from (2)
(2) +35a+%2B+45b+=+630+
(1) +-35a+-+35b+=+-560+
+10b+=+70+
+b+=+7+
and, since
(1) +a+%2B+b+=+16+
(1) +a+%2B+7+=+16+
(1) +a+=+9+
The number sold @ $35 each is 9
The number sold @ $45 each is 7