Question

In the 1st room of 150 people the ratio of boys to girls is 7:8 while in the second room of 130 people, the ratio is 6:7. What is the new ratio of boys to girls be if the people in the two rooms will be combined?

Answer 1

\(\Large \color{purple}{\rightarrow 150 = 7x + 8x }\)
\(\Large \color{purple}{\rightarrow 150 = 15x }\)
\(\Large \color{purple}{\rightarrow x = 10 }\)

In the first room, there are 70 boys and 80 girls.

\(\Large \color{purple}{\rightarrow 130 = 6x + 7x }\)
\(\Large \color{purple}{\rightarrow 130 = 13x }\)
\(\Large \color{purple}{\rightarrow x = 10 }\)

In the second room, there are 60 boys and 70 girls.

Boys -> 60 + 70 = 130
Girls -> 70 + 80 = 150

The new ratio formed is:

\(\Large \color{purple}{\rightarrow 130:150 }\) or \(\Large \color{purple}{\rightarrow 13:15 }\)