A certain machine running at a constant speed sorts

Question

A certain machine running at a constant speed sorts r letters in t hours at a cost of c dollars per hour. At these rates, what is the total cost, in dollars, of running this machine to sort s letters? A. \frac{stc}{r} B. \frac{src}{t} C. \frac{rtc}{s} D. \frac{sc}{rt} E. \frac{rc}{st} gmatprep_1.png

whatsarc · Accepted Answer

To determine the total cost, in dollars, of running the machine to sort $ s $ letters, we need to understand the relationship between the variables provided: - $ r $: the number of letters sorted per hour - $ t $: the number of hours taken to sort $ r $ letters - $ c $: the cost in dollars per hour to run the machine First, let's find the sorting rate of the machine, which is the number of letters it sorts per hour. Since the machine sorts $ r $ letters in $ t $ hours, the sorting rate is given by: \  Next, we need to determine the time required to sort $ s $ letters. If the machine sorts $ \frac{r}{t} $ letters per hour, the time $ T $ required to sort $ s $ letters is: \  Now, we can calculate the total cost of running the machine for this time. The cost per hour is $ c $ dollars, and the total time required is $ \frac{s \cdot t}{r} $ hours. Therefore, the total cost $ C $ is: \  Simplifying the expression, we get: \  Thus, the total cost, in dollars, of running the machine to sort $ s $ letters is: \

MartyMurray · Answer

A certain machine running at a constant speed sorts  r  letters in  t  hours at a cost of  c  dollars per hour. At these rates, what is the total cost, in dollars, of running this machine to sort  s  letters?

We know that the cost per hour is  c . So, the cost to sort  s  letters is the number of hours needed  × c .

We don't have the number of hours needed for sorting  s  letters. However, we do know the number of hours needed for sorting  r  letters, which is  t .

So, in terms of  r  and  t , the number of hours needed for sorting  s  letters is  \frac{s}{r} × t .

Thus, the total cost of sorting s letters is  \frac{s}{r} × t × c .

A.  \frac{stc}{r}

B.  \frac{src}{t}

C.  \frac{rtc}{s}

D.  \frac{sc}{rt}

E.  \frac{rc}{st}

Correct answer:  A

sujoeku · Answer

Hello - I approached it using units to guide my thinking:

I want to get "dollars"

1) First to cancel out S "letters" I multiplied S letters by (t hours/r letters) <- this was given in the original problem
2) I have (ST)/r so next I need to cancel out "hours" which can be done by multiplying by c$/hours <- this was also given

Therefore the final expression to get "dollars" of S letters is (STC)/R, answer A

A certain machine running at a constant speed sorts

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A ­certain machine running at a constant speed sorts

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A certain machine running at a constant speed sorts