SOLUTION: A machine requires four hours to make a unit of product A and nine hours to make a unit of product B, Last month the machine operated for 333 hours, producing a total of 47 units.

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Question 1014878: A machine requires four hours to make a unit of product A and nine hours to make a unit of product B, Last month the machine operated for 333 hours, producing a total of 47 units. How many units of product A and product B were produced.
Answer by ikleyn(52787) About Me  (Show Source):
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A machine requires four hours to make a unit of product A and nine hours to make a unit of product B,
Last month the machine operated for 333 hours, producing a total of 47 units.
How many units of product A and product B were produced.
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Let n = # of units of the product A produced,
and m = # of units of the product A produced.

So, m and n are those unknowns the problem is asking for.

Then we have this system of two equations in two unknowns, m and n:

 m +  n =  47,   (1)
4m + 9n = 333.   (2)

To solve it, multiply the equation (1) by 4 and then distract it from equation (2). You will have

9n - 4n = 333 - 4*47,   or

5n = 145.

Hence, n = 145%2F9 = 29.

Thus 29 units of the product A were produced, and 47 - 29 = 18 units of the product B.