The owner of Snack Shack mixes cashews worth $5.75 a pound with peanuts worth$2.30 a pound to get a half-pound, mixed-nut bag worth $1.90, How much of each kind of nut is included in the mixed bag? 2 Answers Jun 23, 2018 $\frac{5}{23}$pounds of cashews, $\frac{13}{46}$pounds of peanuts Explanation: I haven't been doing the undated ones lately, but I like nuts. Let $x$be the amount of cashews in pounds, so $\frac{1}{2} - x$is the amount of peanuts. We have $5.75 x + 2.30 \left(\frac{1}{2} - x\right) = 1.90$$575 x + 115 - 230 x = 190$$345 x = 75$$x = \frac{75}{345} = \frac{5}{23}$pounds of cashews $\frac{1}{2} - x = \frac{23}{46} - \frac{10}{46} = \frac{13}{46}$pounds of peanuts Check: 5.75 (5/23) + 2.30 (13/46 ) = 1.9 quad sqrt Jun 23, 2018 Cashew nuts $\frac{5}{23} l b$Peanuts $\frac{13}{46} l b$Explanation: Final blend ->1/2 color(white)()^("lb")" at "$1.90

Let the weight in pound of cashew nuts be $C$ at ($5.75)/(1^("lb")) Let the weight in pound of peanuts be $P$at ("$2.30")/(1^("lb"))

We know that by weight: $P + C = \frac{1}{2} {\textcolor{w h i t e}{}}^{\text{lb}}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{The calculation}}$

$\textcolor{b r o w n}{\text{I will show why this works afterwards - see the graph}}$
$\textcolor{b r o w n}{\text{Basically it is using the slope of a straight line graph}}$

The slope of part is the same as the slope of all

Slope $= \left(\text{Change in cost")/("change in cashew content by weight}\right)$

From the above: 1/2color(white)(.) lbcolor(white)("d") C = $2.875 From the above 1/2color(white)(.) lbcolor(white)("d") P =$1.15

So if all cashew nuts the cost is $2.875 alternatively if all peanuts the cost is $1.15

The $\frac{1}{2}$ lb ( 0.5 lb ) of blend cost will be in between at $1.90 $\frac{2.875 - 1.15}{0.5} = \frac{1.90 - 1.15}{C}$Turn everything up the other way to get the $C$on the top $\textcolor{b r o w n}{\text{Using fractions to give an exact value}}$$\frac{\frac{1}{2}}{1.725} = \frac{C}{\frac{3}{4}}$$C = \frac{1}{2} \times \frac{3}{4} \times \left[\frac{1}{1.724} \times \frac{1000}{1000}\right]$$C = {\cancel{3}}^{1} / 8 \times \frac{1000}{{\cancel{1725}}^{575}} = \frac{5}{23} l b$Thus $P = \frac{1}{2} - \frac{5}{23} = \frac{13}{46} l b\$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~