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A machine, working at a constant rate, manufactures 36 staplers in 28 [#permalink]

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13 Mar 2015, 03:16

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This post received KUDOS

A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125 B. 128 C. 135 D. 144 E. 150

Ans: C. How? Well the machine makes 36 staplers in 28 mins. That means every minute it makes 36/28 = 9/7 staplers. It essentially means that it makes more than ~1.2 staplers a min. 1hr 45min is 60mins + 45mins = 105mins

so to rephrase the question, how many staplers can the machine (which makes ~1.2 or 9/7 staplers a min) make in 105 mins?

Change 1 hr 45 min to 105 min. For this, we need to set up a simple proportion of staplers per time 36/28 = S/105

The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can and can’t cancel in a proportion, see this post. We can cancel the factor of 4 in the 36 and 38. 9/7 = S/105

We absolutely cannot cancel any factors between the 9 and 105. That kind of “cross-canceling” is 100% illegal in a proportion. We can cancel the common factor of 7 in the two denominators. 9/1 = S/15.

Now that the fraction is entirely simplified, we can cross-multiply. S = 9*15 = 135

This question is essentially about ratios, so the math can be done in a variety of ways (using fractions, decimals, percents, etc.). Here's a way to get to the correct answer with a little less "math work"

We're told that a machine manufactures 36 staplers in 28 minutes. We're asked how many staplers would be manufactured in 1 hour and 45 minutes.

1 hour and 45 minutes = 60+45 = 105 minutes

28 does NOT divide evenly into 105, but we can still use some estimation here...

(28 minutes)(4) = 112 minutes, so using this estimate, we'll end up with a total that is a little BIGGER than it should be.

(36 staplers)(4) = 144 staplers. Now, we know that this is TOO BIG, so we're looking for an answer that is a little below 144. With a ratio of 36 staplers per 28 minutes, we know that a little more than 1 stapler is made per minute. Since we're dealing with a calculation that is 7 minutes TOO BIG, the difference in staplers would have to be a little more than 7.

A machine, working at a constant rate, manufactures 36 staplers in 28 minutes. How many staplers does it make in 1 hr 45 min?

A. 125 B. 128 C. 135 D. 144 E. 150

Kudos for a correct solution.

We can solve this using equivalent ratios

We're comparing machine output (measured in # of staplers) with time (in minutes)

1 hr 45 min = 105 minutes Let x = # of staplers that can be made in 105 minutes

We get: 36/28 = x/105 Cross multiply to get: (28)(x) = (36)(105) Divide both sides by 28 to get: x = (36)(105)/(28) To calculate this, it's useful to recognize that 105 = (7)(15) and 36 = (4)(9) and 28 = (4)(7) So, we get: x = (4)(9)(7)(15)/(4)(7) Simplify to get: x = (9)(15) = 135

Answer: C

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Re: A machine, working at a constant rate, manufactures 36 staplers in 28
[#permalink]
11 Jan 2018, 07:12