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unit rate word problem

In 2 1/4 hours, nick wrote 36 text messages.  What was his unit rate during that time?
a) 14 messages per hour
b) 16 messages per hour
c) 34 messages per hour
d) 81 messages per hour

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David S. | Wise Math TutorWise Math Tutor
5.0 5.0 (60 lesson ratings) (60)
Andrea...The answer is b (16) set it up as a proportion problem.
Messages over Time 36/2.25 = x/1 where x will be # of messages in 1 hour
Cross multiply 2.25x = 36.
Divide each side of the equation by 2.25 x = 36/2.25 = 16


oh thanks.  why don't I have to change the fraction into a whole number then multiply? 9/4 x 36/1
Hello again Andrea.  When answering a problem like this 1st get an idea in your head what a reasonable answer would be.  When I see that he texted 36 times in 2 1/4 hours I can estimate pretty quickly that he is texting less than half that amount in only one hour.  That eliminates c and d immediately.  Now to get the exact answer I need to set up a proportion but when I do that I have to make sure that I have the same things in both numerators and the other thing in both denominators.  I am going to choose to put number of text messages in the numerators(one is 36 and the other is unknown and we will call "x".  I am going to put time in each denominator(one is 2 1/4 hours and the other is 1 hour because they asked for a unit rate).  So now I have two fractions that are equivalent(36/2.25 and x/1).  I cross multiply and solve for my unknown "x".  x times 2.25 = 36 times 1.  x = 36/2.25 = 16.  I could have used 9/4 like you wanted.  Then it would have been 36/(9/4) = x/1.  Then cross multiplying I would get x times 9/4 = 36 times 1.  Now you would solve by multiplying each side by the reciprocal (4/9).
(9/4)(4/9)x = (36)(4/9) yielding x = 16.  Hope this helps.  If you need any further explanation let me know.