Question 933630
Austin's mixture is 3/(3+5)=3/8 frozen juice
Madeline's mixture is 1/(1+4)=1/5 frozen juice
The real recipe is 1/(1+3)=1/4 frozen juice
Let x=amount of Austin's mixture needed
Let y=amount of Madeline's mixture needed
Now we know that the amount of pure frozen juice that exists before the mixture takes place ((3/8)x+(1/5)y) has to equal the amount of frozen juice in the final mixture ((1/4)(x+y)).  Soooo our equation is:
(3/8)x +(1/5)y=(1/4)(x+y) multiply each term by 40
15x+8y=10x+10y
5x=2y
x=(2/5)y
So, for every 5 gal of Madeline's mixture, we need (2/5)*5=2 gal of Austin's mixture
CK
Let's say Madeline used 40 gal, then Austin would need to use(2/5)*40=16 gal
(3/8)*16+(1/5)*40=(1/4)*56
6+8=14
14=14

Hope this helps---ptaylor