Question

At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?A. 80B. 90C. 100D. 110E. 120

Answer 1

Answer: E. 120

The number of seniors were there in high school X at the beginning of the year = 120

Step-by-step explanation:

Given : At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4.

Let the number of juniors be 3x and the number of seniors be 4x.

Since , during the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X.

i.e. Number of juniors at the end of the year = 3x-10

Number of seniors at the end of the yea = 4x-2(10)=4x-20

At the end of the year, the ratio of juniors to seniors was 4 to 5.

$\Rightarrow\dfrac{3x-10}{4x-20}=\dfrac{4}{5}$

$\Rightarrow5(3x-10)=4(4x-20)$

$\Rightarrow15x-50=16x-80$

$\Rightarrow16x-15x=80-50$

$\Rightarrow x=30$

The number of seniors were there in high school X at the beginning of the year = 4(30)=120

Hence, the correct answer is E. 120 .