Chapter 8.6, Problem 9CYU

a.

To determine

To find : how many pounds of mix nuts selling for $\$4.50$ per pound

Answer to Problem 9CYU

The $m$ pounds of mixed nuts $=\$4.50m$ and $10+m$ pounds of mixed nuts $=\$5\left(10+m\right)$

Explanation of Solution

Given information :

Sara has 10 pound of dried fruit selling for $\$6.25$ per pound.

Pounds of mixed nuts selling for $\$4.50$ per pound and a trial mix selling for $\$5$ per pound.

Let $m=$ the number of pounds of mixed nuts.

  

Calculation :

  $m$ Is the number of pounds of mixed nuts

1 pound of mixed nuts $=\$4.50$

Therefore, $m$ pounds of mixed nuts $=\$4.50m$

And $10+m$ is the number of pounds of trail mix

1 pound of trial mix $=\$5$

Therefore, $10+m$ pounds of mixed nuts $=\$5\left(10+m\right)$

	Pound	Price per Pound	Total Price
Dried Fruit	10	$\$6.25$	$6.25\left(10\right)$
Mixed Nuts	$m$	$\$4.50$	$4.50m$
Trial Mix	$10+m$	$\$5$	$5\left(10+m\right)$

Hence, the $m$ pounds of mixed nuts $=\$4.50m$ and $10+m$ pounds of mixed nuts $=\$5\left(10+m\right)$ .

b.

To determine

To write : a rational equation using the last column of the table

Answer to Problem 9CYU

The rational equation is $6.25\left(10\right)+4.50m=5\left(10+m\right)$

Explanation of Solution

Given information :

Sara has 10 pound of dried fruit selling for $\$6.25$ per pound.

Pounds of mixed nuts selling for $\$4.50$ per pound and a trial mix selling for $\$5$ per pound.

Calculation :

	Pound	Price per Pound	Total Price
Dried Fruit	10	$\$6.25$	$6.25\left(10\right)$
Mixed Nuts	$m$	$\$4.50$	$4.50m$
Trial Mix	$10+m$	$\$5$	$5\left(10+m\right)$

The total price for dried fruit is $6.25\left(10\right)$ .

The total price for mixed nuts is $4.50m$ .

The total price for trial mix is $5\left(10+m\right)$ .

Therefore, the rational equation is $6.25\left(10\right)+4.50m=5\left(10+m\right)$

Hence, the rational equation is $6.25\left(10\right)+4.50m=5\left(10+m\right)$ .

c.

To determine

To solve : the equation to determine how many pounds of mixed nuts are needed

Answer to Problem 9CYU

25 pounds mixed nuts are needed

Explanation of Solution

Given information :

Sara has 10 pound of dried fruit selling for $\$6.25$ per pound.

Pounds of mixed nuts selling for $\$4.50$ per pound and a trial mix selling for $\$5$ per pound.

Calculation :

The equation to determine is $6.25\left(10\right)+4.50m=5\left(10+m\right)$

The pounds of mixed nuts are needed

  $\begin{array}{l}6.25\left(10\right)+4.50m=5\left(10+m\right)\\ 62.5+4.50m=50+5m\\ 5m-4.50m=62.5-50\\ 0.5m=12.5\\ m=\frac{12.5}{0.5}\\ m=\frac{125\cdot 10}{5\cdot 10}\\ m=25\end{array}$

Hence, 25 pounds mixed nuts are needed.