Math problem(translation problem)

[joonkimdds]

This is one of the problem from Kaplan blue book.

Six people went shopping. Five spent $16 each, and the sixth spent $5 more than the average of all six. How much did the last person spend?

I saw the answer with an explanation but I am still confused about this 6th person. Did he spend money twice? Also, r we trying to get +5 dollars before we get the average or after we get the average?

The explanation on the back says

Let x= the amount of the sixth woman spent

x= {[5(16) +x] / 6} +5

But shouldn't this be
x= {[5(16) +(x+5)] / 6} +5

unless 6th person spent money twice, before we get the average and after we get the average.





p.s. This is off the topic but does anyone know how to get the square root of 2601 without using a calculator? becuz it was on the Kaplan blue book. It was about a triangle with 45, 24, hypoteneus and I found out that hypoteneus is square root of 2601. They r using 8:15:17 ratio to find out that hypoteneus is 51 but without knowing the ratio, is there any other way to find it out?

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[paulee1983]

This is one of the problem from Kaplan blue book.

Six people went shopping. Five spent $16 each, and the sixth spent $5 more than the average of all six. How much did the last person spend?

I saw the answer with an explanation but I am still confused about this 6th person. Did he spend money twice? Also, r we trying to get +5 dollars before we get the average or after we get the average?

The explanation on the back says

Let x= the amount of the sixth woman spent

x= {[5(16) +x] / 6} +5

But shouldn't this be
x= {[5(16) +(x+5)] / 6} +5

unless 6th person spent money twice, before we get the average and after we get the average.





p.s. This is off the topic but does anyone know how to get the square root of 2601 without using a calculator? becuz it was on the Kaplan blue book. It was about a triangle with 45, 24, hypoteneus and I found out that hypoteneus is square root of 2601. They r using 8:15:17 ratio to find out that hypoteneus is 51 but without knowing the ratio, is there any other way to find it out?

For the first question I just understand as what the Kaplan said......

for your off topic question, I think the main pt. of the question is require you to recognize the approximate number of the sq. root. (45^2+24^2)^(1/2) would never smaller than 45, nor would it bigger than 55. (from the experience before) So the answer must be within this range, and I believe you should not find 2 very close numbers.

 

[Richnator]

This is one of the problem from Kaplan blue book.

Six people went shopping. Five spent $16 each, and the sixth spent $5 more than the average of all six. How much did the last person spend?

I saw the answer with an explanation but I am still confused about this 6th person. Did he spend money twice? Also, r we trying to get +5 dollars before we get the average or after we get the average?

The explanation on the back says

Let x= the amount of the sixth woman spent

x= {[5(16) +x] / 6} +5

But shouldn't this be
x= {[5(16) +(x+5)] / 6} +5

unless 6th person spent money twice, before we get the average and after we get the average.





p.s. This is off the topic but does anyone know how to get the square root of 2601 without using a calculator? becuz it was on the Kaplan blue book. It was about a triangle with 45, 24, hypoteneus and I found out that hypoteneus is square root of 2601. They r using 8:15:17 ratio to find out that hypoteneus is 51 but without knowing the ratio, is there any other way to find it out?

I think kaplan explained it well. Only thing i can say is that think of X as the sixth person. So, the average spending compared to her is X-5= Average
Average= (5(16)+x)divided by 6)

 

[joonkimdds]

I think kaplan explained it well. Only thing i can say is that think of X as the sixth person. So, the average spending compared to her is X-5= Average
Average= (5(16)+x)divided by 6)

if x= {[5(16) +x] / 6} +5 is correct....
does that mean 6th person spent x amount first and then spent x+5 later?

 

[Richnator]

if x= {[5(16) +x] / 6} +5 is correct....
does that mean 6th person spent x amount first and then spent x+5 later?

No. X= the amount the person spent. The +5 is the amount above average. Think about the problem for a little bit. Basically it is this statement in plain english 6th person= average +5. X= 6th Average=((5(16)+x)/6)

 

[rals]

the point to this question is to try to find different relationships between what's given, ie. different equations.

you need 2 equations to see it clearly:

for the average spent by all:

y={(16x5)+x}/6 get it?

then, we know that the 6th person spent the average amount plus five, so (call the total x):

x=y+5 or y=x-5

now sub y=x-5 into y={(16x5)+x}/6 for y, and you get your answer!