Answer :
We can set up a proportion to solve the problem. If 4 cups of water are needed for every 6 tablespoons of mix, then we can write:
4/6 = 6/x
where x is the number of tablespoons of mix needed for 6 cups of water.
To solve for x, we can cross-multiply:
4x = 6 x 6
4x = 36
x = 9
So, if you want to make 6 cups of Kool-Aid, you should use 9 tablespoons of mix.
Similarly, if you want to make 10 cups of Kool-Aid, you can set up another proportion:
4/6 = 10/x
Cross-multiplying:
4x = 6 x 10
4x = 60
x = 15
Therefore, you should use 15 tablespoons of mix for 10 cups of Kool-Aid.
4/6 = 6/x
where x is the number of tablespoons of mix needed for 6 cups of water.
To solve for x, we can cross-multiply:
4x = 6 x 6
4x = 36
x = 9
So, if you want to make 6 cups of Kool-Aid, you should use 9 tablespoons of mix.
Similarly, if you want to make 10 cups of Kool-Aid, you can set up another proportion:
4/6 = 10/x
Cross-multiplying:
4x = 6 x 10
4x = 60
x = 15
Therefore, you should use 15 tablespoons of mix for 10 cups of Kool-Aid.
for 6 cups of water?
[tex]\begin{array}{ccll} \stackrel{cups}{water}&\stackrel{tspoons}{mix}\\ \cline{1-2} 4 & 6\\ 6& x \end{array} \implies \cfrac{4}{6}~~=~~\cfrac{6}{x} \\\\\\ \cfrac{ 2 }{ 3 } ~~=~~ \cfrac{ 6 }{ x }\implies 2x=18\implies x=\cfrac{18}{2}\implies x=9[/tex]
how about for 10?
[tex]\begin{array}{ccll} \stackrel{cups}{water}&\stackrel{tspoons}{mix}\\ \cline{1-2} 4 & 6\\ 10& y \end{array} \implies \cfrac{4}{10}~~=~~\cfrac{6}{y} \\\\\\ \cfrac{ 2 }{ 5 } ~~=~~ \cfrac{ 6 }{ y }\implies 2y=30\implies y=\cfrac{30}{2}\implies y=15[/tex]
