Chapter 5.7, Problem 25IP

(a)

To determine

To find:The amount of lime juice in $130$ ounces of punch.

Answer to Problem 25IP

The amount of lime juice in $130$ ounces of punch is $10$ ounces.

Explanation of Solution

Given information:

The following table shows the amount of each ingredient in $52$ ounces of punch:

Ingredient	Amount(ounces)
Lime juice	$4$
Water	$12$
Cranberry concentrate	$12$
Sparkling lemon water	$24$

Calculation:

The constant of proportionality for the amount of Lime Juice per ounce is,

  $\begin{array}{c}\frac{\text{Amount of lime juice}}{\text{Number of ounces}}=\frac{4}{52}\\ =\frac{1}{13}\end{array}$

Hence, $\frac{1}{13}$ ounce of lime juice is mixed in each ounce of punch.

Let $x$ be the amount of lime juice and $y$ be the number of punches.

The amount of lime juice is calculated as,

  $x=\frac{1}{13}y$

Substitute $130$ for $y$ in the above equation.

  $\begin{array}{c}x=\frac{1}{13}y\\ =\frac{1}{13}\times 130\\ =10\end{array}$

Therefore, the amount of lime juice in $130$ ounces of punch is $10$ ounces.

(b)

To determine

To find:The amount of cranberry concentrate contained in the punch when $54$ ounces of sparkling lemon water are in the punch.

Answer to Problem 25IP

The amount of cranberry concentrate contained in the punch is $27$ ounces.

Explanation of Solution

Given information:

The following table shows the amount of each ingredient in $52$ ounces of punch:

Ingredient	Amount(ounces)
Lime juice	$4$
Water	$12$
Cranberry concentrate	$12$
Sparkling lemon water	$24$

Calculation:

The constant of proportionality for amount of sparkling lemon water per ounce of punch is,

  $\begin{array}{c}\frac{\text{amount of sparkling lemon water}}{\text{number of ounces}}=\frac{24}{52}\\ =\frac{6}{13}\end{array}$

Hence, $\frac{6}{13}$ ounces of sparkling lemon water in per ounce of punch.

Let $x$ be the amount of sparkling lemon water and $y$ be the number of punches.

The amount of sparkling lemon water is calculated as,

  $x=\frac{6}{13}y$

Substitute $54$ for $x$ in the above equation.

  $\begin{array}{c}x=\frac{6}{13}y\\ 54=\frac{6}{13}y\\ y=54\times \frac{13}{6}\\ y=117\end{array}$

So, the number of ounces is $117$ .

The constant of proportionality for amount of cranberry concentrate per ounce of punch is,

  $\begin{array}{c}\frac{\text{Amount of cranberry concentrate}}{\text{Number of ounces}}=\frac{12}{52}\\ =\frac{3}{13}\end{array}$

Hence, $\frac{3}{13}$ ounces of cranberry concentrate in per ounce of punch.

Let $x$ be the amount of cranberry concentrate and $y$ be the number of punches.

The amount of cranberry concentrate is calculated as,

  $x=\frac{3}{13}y$

Substitute $117$ for $y$ in the above equation.

  $\begin{array}{c}x=\frac{3}{13}y\\ x=\frac{3}{13}\times 117\\ x=27\end{array}$

Therefore, the amount of cranberry concentrate contained in the punch is $27$ ounces.

(c)

To determine

To find:The number of ounces of punch if the punch contains $44$ ounces of water.

Answer to Problem 25IP

The number of ounces of punch if the punch contains $44$ ounces of water is $190\frac{2}{3}$ .

Explanation of Solution

Given information:

The following table shows the amount of each ingredient in $52$ ounces of punch:

Ingredient	Amount(ounces)
Lime juice	$4$
Water	$12$
Cranberry concentrate	$12$
Sparkling lemon water	$24$

Calculation:

The constant of proportionality for amount of water per ounce of punch is,

  $\begin{array}{c}\frac{\text{Amount of water}}{\text{Number of ounces}}=\frac{12}{52}\\ =\frac{3}{13}\end{array}$

Hence, $\frac{3}{13}$ ounce of water per ounce of punch.

Let $x$ be the amount of water and $y$ be the number of punches.

The amount of water is calculated as,

  $x=\frac{3}{13}y$

Substitute $44$ for $x$ in the above equation.

  $\begin{array}{c}x=\frac{3}{13}y\\ 44=\frac{3}{13}y\\ y=44\times \frac{13}{3}\\ y=190\frac{2}{3}\end{array}$

Therefore, the number of ounces of punch if the punch contains $44$ ounces of water is $190\frac{2}{3}$ .