<PRE><B>Question 314258</B>
A manufacturer produces two models of the same toy: Model A and Model B.
 Model A takes 4 hours to produce and costs $8/each.
 Model B takes 3 hours to produce and costs $7/each. 
If the manufacturer allots a total of 5800 hours and $12,600 for production
 each week, how many of each model will be produced?
:
Let a = no. of A models
Let b = no. of B models
:
the labor equation
4a + 3b = 5800
:
the cost equation
8a + 7b = 12600
:
Multiply the labor equation by 2, subtract from the cost equation
8a + 7b = 12600
8a + 6b = 11600
------------------subtraction eliminates a, find b
b = 1000 ea B model toys
:
find a using the labor equation
4a + 3(1000) = 5800 
4a = 5800 - 3000
4a = 2800
a = {{{2800/4}}}
a = 700 ea A model toys
:
:
Check solutions in the cost equation
700(8) + 1000(7) =
5600 + 7000 = 12,600; confirms our solutions</PRE>