Chapter 11.8, Problem 30PPS

Solution

a.

To complete:

The given table with the data

The completed table is:

Juice	Pints of orange juice	Total pints of juice	Percent of orange juice
Original mixture	$2$	$5$	$0.4$
Final mixture	$2+x$	$5+x$	$0.6$

Given information:

Juice	Pints of orange juice	Total pints of juice	Percent of orange juice
Original mixture		$5$
Final mixture	$2+x$		$0.6$

Explanation:

Consider,

The original mixture is $x$ pints

Addition of orange juice: $2$ pints

Addition of pineapple juice: $3$ pints

Now, the incomplete values are estimated as:

Pints of orange juice: $2$ pints

Total pints of juice are:

Orange juice plus pineapple juice: $2+3=5pt$

Percent of orange juice is the ratio of pints of orange juice and total pints of juice is:

  $\begin{array}{l}\%=\frac{2}{5}\\ \%=0.4\end{array}$

So, the completed table is:

Juice	Pints of orange juice	Total pints of juice	Percent of orange juice
Original mixture	$2$	$5$	$0.4$
Final mixture	$2+x$	$5+x$	$0.6$

b.

To calculate:

The pints of orange juice to add

The pints of orange juice to add are $2.5$ pints.

Given information:

The original mixture is $x$ pints Addition of orange juice: $2$ pints

Addition of pineapple juice: $3$ pints

Explanation:

Consider,

The original mixture is $x$ pints

Addition of orange juice: $2+x$ pints

Total pints of juice: $5+x$ pints

Now need to calculate the value of orange juice pints as:

  $\begin{array}{l}\frac{2+x}{5+x}=0.6\\ 2+x=0.6\left(5+x\right)\\ x=2.5\end{array}$

Therefore, the pints of orange juice to add are $2.5$ pints.