Chapter 5.4, Problem 48HP

To determine

To find:The number of cups of each ingredients needed for recipe of fruit punch.

Answer to Problem 48HP

The number of cups needed for cranberry juice, apple juice, pineapple juice, lemon juice and club soda respectively are $3.8\text{c}$ , $3\text{c}$ , $1.3\text{c}$ , $0.6\text{c}$ and $3.8\text{c}$ .

Explanation of Solution

Given information: Thevolume of cranberry juice in fruit punch is $900\text{mL}$ , volume of apple juice in fruit punch is $700\text{mL}$ ,volume of pineapple juice in fruit punch is $300\text{mL}$ ,volume of lemon juice in fruit punch is $150\text{mL}$ andvolume of club soda in fruit punch is $900\text{mL}$ ,

Calculation:

For Cranberry Juice:

The conversion ofmilliliter into liter is:

  $1\text{mL}=\frac{1}{1000}\text{L}$

To find the conversion of $900\text{mL}$ ,multiply both sides of above conversion by $900$ .

  $\begin{array}{c}900\times 1\text{mL}=900\times \frac{1}{1000}\text{L}\\ =\frac{900}{1000}\text{L}\\ =0.9\text{L}\end{array}$

The conversion of liter into pints is:

  $1\text{L}=2.114\text{pt}$

To find the conversion of $0.9\text{L}$ , multiply both sides of above conversion by $0.9$ .

  $\begin{array}{c}0.9\times 1\text{L}=0.9\times 2.114\text{pt}\\ =1.9026\text{pt}\end{array}$

The conversion of pints into cups is:

  $1\text{pt}=2\text{c}$

To find the conversion of $1.9026\text{pt}$ , multiply both sides of above conversion by $1.9026$ .

  $\begin{array}{c}1.9026\times 1\text{pt}=1.9026\times 2\text{c}\\ =3.8052\text{c}\\ \approx 3.8\text{c}\end{array}$

Therefore, the conversion of cranberry juice of $900\text{mL}$ into cupsis $3.8\text{c}$ .

For Apple Juice:

The conversion of milliliter into liter is:

  $1\text{mL}=\frac{1}{1000}\text{L}$

To find the conversion of $700\text{mL}$ , multiply both sides of above conversion by $700$ .

  $\begin{array}{c}700\times 1\text{mL}=700\times \frac{1}{1000}\text{L}\\ =\frac{700}{1000}\text{L}\\ =0.7\text{L}\end{array}$

The conversion of liter into pints is:

  $1\text{L}=2.114\text{pt}$

To find the conversion of $0.7\text{L}$ , multiply both sides of above conversion by $0.7$ .

  $\begin{array}{c}0.7\times 1\text{L}=0.7\times 2.114\text{pt}\\ =1.4798\text{pt}\end{array}$

The conversion of pints into cups is:

  $1\text{pt}=2\text{c}$

To find the conversion of $1.4798\text{pt}$ , multiply both sides of above conversion by $1.4798$ .

  $\begin{array}{c}1.4798\times 1\text{pt}=1.4798\times 2\text{c}\\ =2.9596\text{c}\\ \approx 3\text{c}\end{array}$

Therefore, the conversion of apple juice of $700\text{mL}$ into cups is $3\text{c}$ .

For Pineapple Juice:

The conversion of milliliter into liter is:

  $1\text{mL}=\frac{1}{1000}\text{L}$

To find the conversion of $300\text{mL}$ , multiply both sides of above conversion by $300$ .

  $\begin{array}{c}300\times 1\text{mL}=300\times \frac{1}{1000}\text{L}\\ =\frac{300}{1000}\text{L}\\ =0.3\text{L}\end{array}$

The conversion of liter into pints is:

  $1\text{L}=2.114\text{pt}$

To find the conversion of $0.3\text{L}$ , multiply both sides of above conversion by $0.3$ .

  $\begin{array}{c}0.3\times 1\text{L}=0.3\times 2.114\text{pt}\\ =0.6342\text{pt}\end{array}$

The conversion of pints into cups is:

  $1\text{pt}=2\text{c}$

To find the conversion of $0.6342\text{pt}$ , multiply both sides of above conversion by $0.6342$ .

  $\begin{array}{c}0.6342\times 1\text{pt}=0.6342\times 2\text{c}\\ =1.2684\text{c}\\ \approx 1.3\text{c}\end{array}$

Therefore, the conversion of pineapple juice of $300\text{mL}$ into cups is $1.3\text{c}$ .

For Lemon Juice:

The conversion of milliliter into liter is:

  $1\text{mL}=\frac{1}{1000}\text{L}$

To find the conversion of $150\text{mL}$ , multiply both sides of above conversion by $150$ .

  $\begin{array}{c}150\times 1\text{mL}=150\times \frac{1}{1000}\text{L}\\ =\frac{150}{1000}\text{L}\\ =0.15\text{L}\end{array}$

The conversion of liter into pints is:

  $1\text{L}=2.114\text{pt}$

To find the conversion of $0.15\text{L}$ , multiply both sides of above conversion by $0.15$ .

  $\begin{array}{c}0.15\times 1\text{L}=0.15\times 2.114\text{pt}\\ =0.3171\text{pt}\end{array}$

The conversion of pints into cups is:

  $1\text{pt}=2\text{c}$

To find the conversion of $0.3171\text{pt}$ , multiply both sides of above conversion by $0.3171$ .

  $\begin{array}{c}0.3171\times 1\text{pt}=0.3171\times 2\text{c}\\ =0.6342\text{c}\\ \approx 0.6\text{c}\end{array}$

Therefore, the conversion of lemon juice of $150\text{mL}$ into cups is $0.6\text{c}$ .

For Lime Soda:

The conversion of milliliter into liter is:

  $1\text{mL}=\frac{1}{1000}\text{L}$

To find the conversion of $900\text{mL}$ , multiply both sides of above conversion by $900$ .

  $\begin{array}{c}900\times 1\text{mL}=900\times \frac{1}{1000}\text{L}\\ =\frac{900}{1000}\text{L}\\ =0.9\text{L}\end{array}$

The conversion of liter into pints is:

  $1\text{L}=2.114\text{pt}$

To find the conversion of $0.9\text{L}$ , multiply both sides of above conversion by $0.9$ .

  $\begin{array}{c}0.9\times 1\text{L}=0.9\times 2.114\text{pt}\\ =1.9026\text{pt}\end{array}$

The conversion of pints into cups is:

  $1\text{pt}=2\text{c}$

To find the conversion of $1.9026\text{pt}$ , multiply both sides of above conversion by $1.9026$ .

  $\begin{array}{c}1.9026\times 1\text{pt}=1.9026\times 2\text{c}\\ =3.8052\text{c}\\ \approx 3.8\text{c}\end{array}$

Therefore, the conversion of lime soda of $900\text{mL}$ into cups is $3.8\text{c}$ .

Therefore, from the above expressions the number of cups needed for cranberry juice, apple juice, pineapple juice, lemon juice and club soda respectively are $3.8\text{c}$ , $3\text{c}$ , $1.3\text{c}$ , $0.6\text{c}$ and $3.8\text{c}$ .