In a box, there are red balls and blue balls.
If one takes away one red ball, then 1/7 of the remaining balls are red.
If one takes away 2 blue balls, then 1/5 of the remaining balls are red.
What is the amount of red and blue balls?
I marked y as red balls and x as blue balls, and we know that x+y is the box, then we take away one red ball from the box. but it is unknown, (x+y)-1 red balls = 1/7 red balls + 6/7 blue balls but it doesn't work and i get a decimal. can someone give me a hint?
$x$ - Number of blue balls
$y$ - Number of red balls
You have two equations:
$$y=\frac15(x+y-2)\\y-1=\frac17(x+y-1)$$
Let $a=x+y$, then by subtracting the second equation from the first one we obtain
$$\frac15(a-2)-\frac17(a-1)=1\\7a-14-5a+5=35\\2a-9=35\\2a=44\\a=22$$
So, the total amount of balls are $22$, now substitute it back:
$$y=\frac15(22-2)=4\\x=22-y=22-4=18$$
The answer is $x=18$ and $y=4$.