Question

a recipe for kool-aid calls for 4 cups of water for every 6 tablespoons of mix.how many tablespoons of mix should you use if you wanted 6 cups of water. what about 10 cups

Answer 1

for 6 cups of water?

`\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`

how about for 10?

`\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`

Answer 2

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.