SOLUTION: please help me solve this word problem the production of a small factory is modeled by x+21/2x(x+5), while the production rate of another factory is modeled by 9x+16/2x(x+5). which

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Question 421455: please help me solve this word problem the production of a small factory is modeled by x+21/2x(x+5), while the production rate of another factory is modeled by 9x+16/2x(x+5). which is a model for the combined production rate of the two factories?
i put / because its a fraction thank you.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
production rate of first factory is (x+21) / (2x*(x+5))
production rate of second factory is (9x+16) / (2x*(x+5))

product rate of both factories combined is additive and equals:
((x+21) / (2x*(x+5))) + ((9x+16) / (2x*(x+5))) = ((x+21) + (9x+16)) / (2x*(x+5))

the fractions can be combined because the denominators are the same.

you can then simplify by combining like terms to get:

combined rate of production equals (10x + 37) / (2x*(x+5))

here's how combining production rates work.

i can product 5 widgets an hour.
you can produce 10 widgets an hour.
together we can produce 15 widgets an hour (my 5 per hour plus your 10 per hour).