SOLUTION: A machine requires 6 hours to make a unit of Product A and 5 hours to make a unit of Product B. Last month the machine operated for 481 hours, producing a total of 89 units. How ma

Question 1199462: A machine requires 6 hours to make a unit of Product A and 5 hours to make a unit of Product B. Last month the machine operated for 481 hours, producing a total of 89 units. How many units of Product A were produced?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A machine requires 6 hours to make a unit of Product A and 5 hours to make a unit of Product B.
Last month the machine operated for 481 hours, producing a total of 89 units.
How many units of Product A were produced?
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            It can be solved using two equations in two unknown, or one equation in one unknown.

            I will show you the last way.

Let x be the number of units of A-product. Then the number of units of B-product is 89-x. Write the full elapsed time equation 6x + 5*(89-x) = 481. Simplify and find x 6x + 445 - 5x = 481 6x - 5x = 481 - 445 x = 36. ANSWER. 36 units of A-product were produced. CHECK. 6*36 + 5*(89-36) = 6*36 + 5*53 = 216 + 265 = 481 hours, total time. ! correct !

Solved.

----------------

Be attentive: in his solution, tutor @greenestamps mixed up products A and B
and gave you wrong answer.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

(Corrected -- in my original response I had the two products switched....)

A quick mental solution, if formal algebra is not required and your mental math is good....

If all 89 units had been Product B, the total machine time would have been 89*5 = 445 hours.
The actual machine time was 81 hours, which is 36 hours more than that.
Since each Product A requires 1 more hour of machine time than each Product B, the number of Product A produced was 36/1 = 36

ANSWER: 36 units of Product A, so 89-36 = 53 units of Product B

CHECK: 53(5)+36(6) = 265+216 = 481

This quick informal method is applicable to a large number of similar problems, like....

75 bicycles and tricycles in a cycle shop with a total of 173 wheels; how many of each are there

63 cows and chickens in a barnyard with a total of 160 legs; how many of each are there

etc....

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