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The ratio of boys to girls in the junior class is 2 to 3 respectively

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Bunuel
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The ratio of boys to girls in the junior class is 2 to 3 respectively [#permalink] New post   24 Jan 2023, 11:10
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The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?

(A) 100
(B) 300
(C) 375
(D) 400
(E) 500
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D
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Re: The ratio of boys to girls in the junior class is 2 to 3 respectively [#permalink] New post   24 Jan 2023, 14:04
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Bunuel wrote:
The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?

(A) 100
(B) 300
(C) 375
(D) 400
(E) 500


Junior Class

\(\frac{B}{G }= \frac{2x }{ 3x}\)

Senior Class

\(\frac{ G}{B }= \frac{7y }{ 3y}\)

Quote:
there are 300 more students in the senior class than in the junior class


( 7y + 3y ) - (2x + 3x) = 300

10y - 5x = 300

2y - x = 60 ----- (1)

Quote:
the combined ratio of boys to girls in both classes is 8 to 17


\(\frac{2x + 3y }{ 3x + 7y} = \frac{8}{17}\)

Solving the equation we get

2x = y ----- (2)

Substituing (2) in (1)

4x - x = 60

x = 20

y = 40

Number of students in the senior class = 10y = 400

Option D
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The ratio of boys to girls in the junior class is 2 to 3 respectively [#permalink] New post   27 Mar 2023, 21:41
The ratio in the junior class is \(\frac{B}{G}\) = \(\frac{2x}{3x}\) and together 5x.
So at the minimum x = 1 and so we have 5 students in the junior class.

Based on the above, the number of students in the senior class is at least 305. The ratio in the senior class is \(\frac{B}{G}\) = \(\frac{3y}{7y}\) and together 10y.
so, if at the minimum there are 5 students in the junior class, then y should at least be 31 (10*31 = 310). However, in the answer choices we've only got 375, 400, and 500.

375 is not possible because then y = 37.5 and we can't have half a boy/girl.

So basically you can start and check from 400.

If senior class = 400 students, then y = 40. Then it means that junior class = 100, x = 20. Plug in and check:

\(\frac{B}{G}\) = (40+120)/(60+280) => 160/340 = 8z/17z ........... => Z/Z = 1 CORRECT.

Answer choice D
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Re: The ratio of boys to girls in the junior class is 2 to 3 respectively [#permalink] New post   28 Mar 2023, 00:04
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Bunuel wrote:
The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?

(A) 100
(B) 300
(C) 375
(D) 400
(E) 500


We can use weighted averages here the way we use in mixtures.

Concentration of boys in junior class =\( \frac{2}{5} = \frac{20}{50}\)
Concentration of boys in senior class = \(\frac{3}{10} = \frac{15}{50}\)
Overall concentration of boys = \(\frac{8}{25} = \frac{16}{50}\)

\(\frac{Ws}{Wj} = \frac{(20 - 16)}{(16 - 15)} = \frac{4}{1}\)

Students in senior class : Students in junior class = 4 : 1
The difference of 3 in ratio terms is 300 so multiplier is 100.
Number of students in senior class = 4 * 100 = 400

Answer (D
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Re: The ratio of boys to girls in the junior class is 2 to 3 respectively [#permalink]
28 Mar 2023, 00:04
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