The ratio of the number of boys and girls in a school is 3:5. If 50 more boys are admitted to the school, then the ratio of the boys to girls changes to 1:1.
What is the number of girls that must be admitted to get to the ratio 5:7 ?
Answers
Answer:
ANSWER IN THE ATTACHMENT ABOVE
Given,
The ratio of the number of boys and girls in a school is 3:5.
50 more boys are admitted to the school, then the ratio of the boys to girls changes to 1:1.
To Find,
the number of girls that must be admitted to get to the ratio of 5:7.
Solution,
Let us assume the common factor is x in the given ratio.
The ratio of boys to girls= is 3x/5x.
When 50 more boys are added, 3x+50/5x.
This is equal to the ratio of 1:1.
therefore, 3x+50/5x= 1/1.
3x+50=5x.
x=25.
The number of girls in class= 5x= 5×25= 125.
The number of boys in class= 3x= 3×25=75.
When 50 more boys are added then the total number of boys= is 75+50= 125.
According to the question, the new ratio is 5:7.
For this let us assume again that the common factor is x.
5x= 125.
7x= 125/5 ×7= 175.
Therefore, the number of girls to be added is 175-125= 50.
Hence, the number of girls to be added is 50.