Word Problem - Need help A.S.A.P.

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shanieO

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Mar 9, 2006
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We are to use elimination and substitution procedure to solve this word problem.

a manufacturer makes two products A and B, each of which is processed in two departments, production and finishing. Each A takes 3 hours to produce and 6 hours to finish, each B takes 5 hours to produce and 2 hours to finish. How many units of A and B can be produced and finished if exactly 24 hours are available in each department and all hours must be used?

This is what I have done:

3x + 5y = 24 * -2 -6x - 10y = -48
6x + 2y = 24 6x + 2y = 24

-8y = -24

y = 3

Substitute y = 3 into 3x + 5y = 24

3x + 5(3) = 24
3x = 24 - 15
x = 3

Is this correct?

Thanks
ShannieO
 
shanieO said:
This is what I have done:

3x + 5y = 24 * -2 -6x - 10y = -48
6x + 2y = 24 6x + 2y = 24
Click to expand...
I'm sorry, but I don't follow. For instance, why does the first equation have two "equals" signs in it?

Please reply with clarification, starting with what "x" and "y" stand for.

Thank you.

Eliz.
 
I multiplied the first equation by -2 so that I could subtract the second equation from it.
First equation is production hours.
Second equation is finish hours.
 
I would suggest that next time you keep it as A & B, not go to x & y. That keeps the variable tied to the problem statement.
Also do one equation per line.
Finally x=A=3 and y=B=3 is correct. Put them both in the original equation and they work!
 
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