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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
(A) 100
(B) 300
(C) 375
(D) 400
(E) 500
24 Jan 2023, 14:04
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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
(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
27 Mar 2023, 21:41
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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
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
