Answer :
boys: x
gilrs: y
From the text of the task:
[tex] \left \{ {{\frac{x}{y}=\frac{5}{7}} \atop {x+y=48 \rightarrow x=48-y}} \right. [/tex]
Replacing x:
[tex]\frac{48-y}{y}=\frac{5}{7}\\ \\ 7(48-y)=5y\\ \\ 336-7y=5y\\ \\ 12y=336\\ \\ y=\frac{336}{12}=28[/tex]
So there are 28 girs and 20 boys
gilrs: y
From the text of the task:
[tex] \left \{ {{\frac{x}{y}=\frac{5}{7}} \atop {x+y=48 \rightarrow x=48-y}} \right. [/tex]
Replacing x:
[tex]\frac{48-y}{y}=\frac{5}{7}\\ \\ 7(48-y)=5y\\ \\ 336-7y=5y\\ \\ 12y=336\\ \\ y=\frac{336}{12}=28[/tex]
So there are 28 girs and 20 boys
Did you say that the ratio of boys to girls is 5 to 7 ?
Well, then we know that 5 'groups' in the cast are boys, and 7 'groups' are girls.
So all together, there are 12 'groups' of students in the play, although we don't know
how many a 'group' is.
But wait a second. You said there are 48 all together. So each 'group' must be
48/12 = 4 students.
5 'groups' of boys = 20 boys
7 'groups' of girls = 28 girls
Check:
-- The ratio of 20 to 28 is 5 to 7 . OK
-- 20 + 28 = 48 all together. OK
It all checks out.
yay
Well, then we know that 5 'groups' in the cast are boys, and 7 'groups' are girls.
So all together, there are 12 'groups' of students in the play, although we don't know
how many a 'group' is.
But wait a second. You said there are 48 all together. So each 'group' must be
48/12 = 4 students.
5 'groups' of boys = 20 boys
7 'groups' of girls = 28 girls
Check:
-- The ratio of 20 to 28 is 5 to 7 . OK
-- 20 + 28 = 48 all together. OK
It all checks out.
yay
