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# At an elementary school, the students in third grade, fourth grade, an

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Math Expert
Joined: 02 Sep 2009
Posts: 58381

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31 Mar 2019, 21:37
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Difficulty:

15% (low)

Question Stats:

84% (02:18) correct 16% (02:45) wrong based on 55 sessions

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At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

A. 12
B. 37/3
C. 88/7
D. 13
E. 14

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01 Apr 2019, 04:05
Bunuel wrote:
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

A. 12
B. 37/3
C. 88/7
D. 13
E. 14

class 3 = a
class 4 = b
class 5= c
a=2b
b=2c
so
12a+15b+10c/a+b+c
solve we get
88/7
IMO C
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10 Apr 2019, 22:58
Bunuel wrote:
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

A. 12
B. 37/3
C. 88/7
D. 13
E. 14

The Q is, Avg #of min/day by all students= Total time taken by students / total #of students

Let's say, 3rd grade student= x

As Q says, Twice as many 3rd graders as 4th graders: x= 2y
We can also say, x= 2*2z= 4z

Total # of students= x+y+z= 4z+2z+z= 7z

Total time taken by all students= 12x+15y+10z= 12*4z+15*2z+10*z = 88z

Going back to the formula: 88z/7z = 88/7 is our ans.
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10 Apr 2019, 23:26
Bunuel wrote:
At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of 12, 15, and 10 minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these students?

A. 12
B. 37/3
C. 88/7
D. 13
E. 14

Let the number of 3rd Graders be A
Let the number of 4th Graders be B
Let the number of 5th Graders be C

According to the question,
$$A=2B$$
$$B=2C$$

If we assume C to be 1, then
$$B=2$$
$$A=4$$

Taking the average
$${12(4) + 15(2) + 10(1)}$$ / $${1+2+4}$$

=$$\frac{88}{7}$$
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Re: At an elementary school, the students in third grade, fourth grade, an   [#permalink] 10 Apr 2019, 23:26
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