A bottle manufacturing company has 5 identical machines, each of which produces bottles at the same constant rate. How many bottles will all 5 machines produce running simultaneously for x hours?
(1) Running simultaneously, 3 of the machines produce 72,000 bottles in 2x hours?
(2) Running simultaneously, 2 of the machines produce 24,000 bottles in x hours?
Once you have the bottles produced by 1 machine in x hours, you can easily find the bottles produced by 5 machines in x hrs. Each statement independently gives you the bottles produced by 1 machine in x hrs so each statement alone is sufficient.
Though you don't need to find the actual number of bottles in this case, if you do need to in PS questions, you can use a quick one step process for such work problems. The advantage of doing it in one step is that sometimes, these fractions cancel each other out and your calculations are reduced.
Question: 3 of the machines produce 72,000 bottles in 2x hours. How many bottles will all 5 machines produce running simultaneously for x hours?
You need to find the number of bottles. So
2x hrs becomes x hrs. The number of hrs has reduced so number of bottles made will reduce. You multiply 72000 by a number less than 1.
72000 * (1/2)
3 machines have become 5 machines. More machines will make more bottles. So multiply by 5/3, a number more than 1.
72000 * (1/2) * (5/3) = 60,000
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