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**Review:**Machines and Combined Rate

Explanation

Rates are best expressed in fractions with units. The rate
of the 6 equal machines is

where *R *is the rate
of one machine working, since all machines work at an equal rate. To find the
rate for 14 machines, not 6, we can multiply both sides of the equation by :

We now have 14 machines on the left as we want. The right
side is going to give us 6 hours on the right if we multiply it out, but we
want 3 hours, so we can multiply the right side by 1 ...

For 14 machines, we have 231 widgets in 3 hours.

We can make an estimate to check that this is in the
ballpark. The original 6 machines made 33 widgets in 1 hour. And 14 is more
than double the number of machines, so they are doing something over 66 widgets
an hour. And they are working for 3 hours, so the result will be something like
66 or 70 times 3, so around 210 widgets per hour. Indeed, we could have used
that method to start and gotten the answer very quickly, because there is only
one answer choice even close to the estimate.

The correct answer is (B).

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