Problem Solving

AbeNeedsAnswers wrote:What's the fastest way to answer this question?

Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?

A) $52
B) $117
C) $130
D) $180
E) $234

D

TOTAL HOURS worked = 15 + 20 + 30 = 65 HOURS
TOTAL PAID = $780

RATE of pay = $780/65 hours = $12/hour

Makoto worked for 15 hours.
So, Makoto's payment = (15 hours)($12/hour) = $180

AnswerL D

Hi AbeNeedsAnswers,

There are a variety of different ways to go about solving this problem. The question specifically uses the word "proportionally", so you could take advantage of the built-in ratios and solve it that way. In addition, the answer choices are 'spaced out' enough that we can use some estimation and avoid some of the specific calculations that you might use in other approaches.

The three people worked a total of 15+20+30 = 65 hours and Makoto worked 15 of those hours. Thus, he/she worked....

15/65 = 3/13 of the total hours

We're told that the workers are paid proportionally based on the number of hours worked. 3/12 = 1/4, so 3/13 is a little less than 1/4.

1/4 of $780 = $195

So we're looking for an answer that's a little less than $195. There's only one answer that fits....

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote:What's the fastest way to answer this question?

Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?

A) $52
B) $117
C) $130
D) $180
E) $234

D

This is a typical question on Ratio and Proportion.

Since each was paid in proportion to the number of hours he or she worked, $780 should be distributed in the ratio of 15 : 20 : 30, where 15 represents the share of Makoto.

On a ratio scale the total payment = 15 + 20 + 30 = 65

Thus, the share of Makoto = (15/65)*780 = $180.

The correct answer: D

Hope this helps!

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AbeNeedsAnswers wrote:What's the fastest way to answer this question?

Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. If Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, how much was Makoto paid?

A) $52
B) $117
C) $130
D) $180
E) $234

We are given that Makoto, Nishi, and Ozuro were paid a total of $780 for waxing the floors at their school. Each was paid in proportion to the number of hours he or she worked. Since Makoto worked 15 hours, Nishi worked 20 hours, and Ozuro worked 30 hours, we can create the following proportion:

Makoto payment : Nishi payment : Ozuro payment = 15x : 20x : 30x

We can create the following equation to determine x:

15x + 20x + 30x = 780

65x = 780

x = 12

Since x = 12, Makoto was paid 15 x 12 = 180 dollars.

Alternate Solution:

Since we know that Makoto's payment was equivalent to 15x, we know that his payment must be a multiple of 15. Since 180 is the only multiple of 15, the correct answer must be 180.

Answer: D