Algebra word problem

Question

Sweder's hardware carries k yards of oak which sell for $3.75 a yard and m yards of maple which sells for $4.50 a yard. When a builder asks for a mixture of two kinds of wood, Sweder's sells him 50 yards at a price of $4 a yard. Find out the number of yards of each kind of wood the builder received.

Answer 1

this is a new one...selling lumber by the yard (it was always by the linear ft, in my experience).

But at this lumberyard, one can say that the averaqe price 4 comes from fraction x times 3.75 plus (1-x) times 4.50, that is, 3.75x + 4.5(1-x) = 4.  Solve for x. Then apply this x factor to 50 to find yds of oak, and apply the (1-x) factor to 50 to find the yds of maple.