Hello!
a.) We can use a system here to solve this.
Let x=amount of red potion used
Let y=total amount of potion in solution
\(200+x=y \)
\(.15(200)+.75x=.25y\)
.15(200) because 15% of the blue potion=.15 and there is 200mL.
.75x because 75% of the red potion=.75 and there is x amount of it
.25y because we want 25% of the total potion=.25 and there is y amount of it
We can substitute for y in the second equation:
\(.15(200)+.75x=.25(200+x)\)
Simplify:
\(30+.75x=50+.25x\)
\(-20=-.5x\)
\(x=40\)
Knowing that x=40, we know that y=240, meaning our answer is 240.
b.) We can again use a system for this problem
Let x=Amount of red potion
Let y=Amount of blue potion
\(x+y=400 \)
\(.3(400)=.15y+.75x\)
.3(400)=30% of the 400 mL
.15y=15% of the magic syrup
.75x=75% of the magic syrup
We can substitute for x in this equation:
\(120=.15y+.75(400-y)\)
Simplify:
\(120=.15y+300-.75y\)
\(-180=-.6y\)
\(y=300, x=100\)
There are 300 mL of blue potion used and 100 mL of red potion used.
c.) Let x=amount of red potion
Let y=amount of blue potion
\(.15x+.75y=.35(x+y)\)
.35(x+y) because the total amount of the potion is x+y
Simplify:
\(.15x+.75y=.35x+.35y\)
\(.4y=.2x\)
\(2y=x\)
Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
For example, 200 mL of blue potion and 100 mL of red potion would work.
Hope this helps!
