Question

Help please. Catching up on missed work from being out due to medical issues. Thank you in advance!

Answer 1

Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.

Therefore, we can set the following equation:

`\begin{gathered} B+I=3, \\ 220B+32I=110\cdot3. \end{gathered}`

Subtracting B from the first equation we get:

`\begin{gathered} B+I-B=3-B, \\ I=3-B\text{.} \end{gathered}`

Substituting the above equation in the second one we get:

`220B+32(3-B)=330.`

Simplifying the above result we get:

`\begin{gathered} 220B+96-32B=330, \\ 188B+96=330. \end{gathered}`

Subtracting 96 to the above equation we get:

`\begin{gathered} 188B+96-96=330-96, \\ 188B=234. \end{gathered}`

Dividing the above equation by 188 we get:

`\begin{gathered} (188B)/(188)=(234)/(188), \\ B\approx1.24. \end{gathered}`

Substituting B=1.24 at I=3-B we get:

`I=3-1.24=1.76.`

Answer:

`\begin{gathered} 1.26\text{ cups of boiling water.} \\ 1.74\text{ cups of ice.} \end{gathered}`