systems of eqns: There are 25 students in a ratio of....

[Donna Henderson]

There are 25 students in a class. The ratio of girls to boys is 2:3. Find out how many boys there are.

I have this information:

x=boys
y=girls

2y=3x
x+y=25

I am getting that there are 10 boys and 15 girls. I know this is wrong and I guess it is because I have the wrong equation, 2y=3x. It works out correctly if I set 2x=3y, but I don't know why. I have to use systems to solve this problem.

 

[stapel]

x=boys
y=girls

2y=3x
x+y=25

I understand where "x + y = 25" came from: "the sum of the number of boy and the number of girls is twenty-five". But how did you get "2y = 3x", given that y/x, the ratio of girls to boys, is ("equals") 2/3?

Please be specific. Thank you.

Eliz.

 

[Donna Henderson]

Ok, so I guess the equation 2y=3x is wrong. Can you tell me what the second equation should be?

 

[soroban]

Hello, Donna!

There are 25 students in a class. The ratio of girls to boys is 2:3.
Find out how many boys there are.

I would do it like this . . .

Let \(\displaystyle B\) = number of boys.
Let \(\displaystyle G\) = number of girls.

"There are 25 students in a class" \(\displaystyle \;\;B\,+\,G\:=\:25\;\) [1]

"The ratio of girls to boys is 2:3" \(\displaystyle \;\;\frac{G}{B}\:=\:\frac{2}{3}\;\;\Rightarrow\;\;3G\:=\:2B\;\;\Rightarrow\;\;2B\,-\,3G\:=\:0\;\) [2]

Multiply equation [1] by 3: \(\displaystyle \:3B\,+\,3G\:=\:75\)
. . . . . . Add equation [2]: \(\displaystyle \:2B\,-\,3G\:=\;0\)

. . . . . . . . . . and we get: . . . . . \(\displaystyle 5B \:=\:75\;\;\Rightarrow\;\;\fbox{B\:=\:15}\)

 

[stapel]

...given that y/x, the ratio of girls to boys, is ("equals") 2/3....

Can you tell me what the second equation should be?

Um... possibly "y/x = 2/3"...?

Eliz.