SOLUTION: An office is equipped with two card-sorting machines, A and B. If A is operated for 2 min and B for 5 mins, 20,500 cards can be sorted. If A is operated for 5 min and B for 2 min,

Question 1129073: An office is equipped with two card-sorting machines, A and B. If A is operated for 2 min and B for 5 mins, 20,500 cards can be sorted. If A is operated for 5 min and B for 2 min, 25000 can be sorted. What are the sorting rates of the machines?
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

(1)
(2)

There are numerous ways to solve the pair of equations....

I will show you an unorthodox method that works nicely with this particular example. It works because adding the two given equations gives us a very useful third equation.

Add the two equations:

(3)

Now use this equation with either of the original equations to eliminate one variable and solve for the other:

Then substitute that value in any of the earlier equations to solve for the other variable.

ANSWER: A sorts 4000 cards per minute; B sorts 2500 cards per minute.

CHECK:
2A+5B = 8000+12500 = 20500
5A+2B = 20000+2500 = 25000

Note that the usual method for solving a pair of equation in the given form would be direct elimination, using the two given equations. But because of the symmetry of the coefficients, it is possible to get the value of A+B and use that to finish solving the pair of equations -- with less work than required by direct elimination.

Finally note that another similar method would be to subtract (1) from (2), allowing you to find a value for A-B; then you could use that in a similar manner to finish solving the pair of equations.
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