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# On a certain high school athletic team, the ratio of freshmen to sopho

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Math Expert
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Posts: 55668
On a certain high school athletic team, the ratio of freshmen to sopho  [#permalink]

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23 Oct 2018, 22:07
00:00

Difficulty:

5% (low)

Question Stats:

94% (01:04) correct 6% (00:51) wrong based on 45 sessions

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On a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. If there are 60 juniors on the team, how many students in total are on the team?

A. 90
B. 140
C. 150
D. 180
E. 210

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Re: On a certain high school athletic team, the ratio of freshmen to sopho  [#permalink]

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23 Oct 2018, 23:07
Bunuel wrote:
On a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. If there are 60 juniors on the team, how many students in total are on the team?

A. 90
B. 140
C. 150
D. 180
E. 210

f:so:j:s = 1:3:4:6
4x=j=60
x=15
total = 15 + 45 + 60 + 90 = 210
E
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Re: On a certain high school athletic team, the ratio of freshmen to sopho  [#permalink]

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23 Oct 2018, 23:17
Bunuel wrote:
On a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. If there are 60 juniors on the team, how many students in total are on the team?

A. 90
B. 140
C. 150
D. 180
E. 210

$$\frac{60}{4}*14 = 210$$, Answer must be (E)
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Re: On a certain high school athletic team, the ratio of freshmen to sopho  [#permalink]

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24 Oct 2018, 03:39

Solution

Given:
• The ratio of freshmen to sophomores to juniors to seniors in the athletic team = 1: 3: 4: 6
• Number of juniors in the team = 60

To find:
• The total number of students in the team

Approach and Working:
• Let us assume that 14x as the total number of students in the team (Since, 1 + 3 + 4 + 6 = 14)
• Thus, number of juniors = 4x = 60
o Implies, x = 15
• Therefore, total number of students in the team = 14 * 15 = 210

Hence the correct answer is Option E

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Re: On a certain high school athletic team, the ratio of freshmen to sopho  [#permalink]

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28 Oct 2018, 18:21
Bunuel wrote:
On a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. If there are 60 juniors on the team, how many students in total are on the team?

A. 90
B. 140
C. 150
D. 180
E. 210

The entire ratio can be expressed as: 1x + 3x + 4x + 6x = total. For the juniors, we can create the equation:

4x = 60

x = 15

So there are 1x + 3x + 4x + 6x = 14x = 14(15) = 210 students on the team

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Re: On a certain high school athletic team, the ratio of freshmen to sopho   [#permalink] 28 Oct 2018, 18:21
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