Alan G. answered • 03/30/16
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Let a be the number of Model A and b the number of Model B. Then you have the equation a + b = 11.
Assuming all 11 presses are being used to produce the 780 records per hour, the total number of records produced with a of Model A and b of Model B would be:
90a + 60b = 780.
You now need to solve the system of linear equations,
a + b = 11
90a + 60b = 780.
I assume you can take it from here. If not, post another reply and someone will offer more help.
Alan G.
Kay,
You could use either method to solve this system. As a rule of thumb, the substitution method works best when one equation has variables with coefficients 1 or -1 (like the first equation). When neither equation has this, the elimination method works best.
The first equation has no numbers in front of a or b because they represent the number of record pressers of each type. When you add them together, you get the total number of record presses. It is understood that the numbers in front of a and b are both 1: 1a = a.
Here is how to get started. Solve a + b = 11 for b: b = 11 - a. Plug this into the second equation:
90a + 60(11 - a) = 780.
Now, you can solve this for a after a little algebraic simplification. Once you get a, you can plug that into the equation for b to get b. And, you should check your answers in both equations from the beginning just to make sure you haven't made any mistakes.
If you really want to use elimination, you could achieve the same result by multiplying a + b = 11 by -60 and adding to the second equation, which will eliminate b, let you solve for a, and you can finish as before.
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03/30/16
Nathan G.
03/30/16