SOLUTION: Hi, could someone please help me to understand this problem? A wood company can convert logs into lumber or plywood. The mill turns out three times as many units of plywood as l

Question 148153: Hi, could someone please help me to understand this problem?
A wood company can convert logs into lumber or plywood. The mill turns out three times as many units of plywood as lumber. A profit of $20 on a untit of lumber and $50 on plywood. How many of each unit must be produced and sold in order to make a profit of $17,680?
Math is my worst subject and I have a very hard time understanding it.
Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A wood company can convert logs into lumber or plywood.
The mill turns out three times as many units of plywood as lumber.
P and L are the number of units of Plywood and of Lumber.
Quantity EQUATION: P = 3L
---------------
A profit of $20 on a unit of lumber and $50 on plywood. How many of each unit must be produced and sold in order to make a profit of $17,680?
Value EQUATION: 50P + 20L = 17680
------------------------------------
Rearrange:
P - 3L = 0
50P + 20L = 17680
--------------------
Modify to allow elimination:
50P - 150L = 0
50P + 20L = 17680
-----------------------
Subtract 1st from 2nd so you can solve for "L":
170L = 17680
L = 104 (number of units of Lumber)
Since P = 3L, P = 312 (number of units of Plywood)
==========================
Cheers,
Stan H.

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