# Question 9c89b

May 30, 2017

$20$ lbs of nuts to be mixed with $40$ lbs of raisins .

#### Explanation:

Let nuts combined is $x$ lb , then raisin combined is $\left(60 - x\right)$ lb

Cost of nuts is $6x , Cost of raisin is $(3(60-x)).
Hence Cost of nuts ans raisins is 6x + 180 -3x = $(3x+180) , Selling price of mix is 60*4=$240

$\therefore 3 x + 180 = 240 \mathmr{and} 3 x = 60 \mathmr{and} x = 20 \therefore 60 - x = 60 - 20 = 40$

Hence $20$ lbs of nuts to be mixed with $40$ lbs of raisins . [Ans]

May 30, 2017

$\textcolor{b l u e}{\text{A different method.}}$

Raisons $\to 40 \textcolor{w h i t e}{.} l b$
Nuts $\text{ } \to 20 \textcolor{w h i t e}{.} l b$

#### Explanation:

If you have all nuts then the cost per pound is $6 If you have all raisons then the cost per pound is$3

The target blend will give a cost per pound of $4 The change in cost has a direct relationship to the proportion of nuts in the blend. Thus we can plot a straight line graph linking blend cost to the weight of nuts in the blend. The slope (gradient) for part of it is the same as that for all of it Let the unknown weight of nuts be $n$Then gradient is such that: $\frac{n \textcolor{w h i t e}{.} l b}{4 - 3} = \frac{60 \textcolor{w h i t e}{.} l b}{6 - 3}$$n = \frac{60 \textcolor{w h i t e}{.} l b}{3} = 20 \textcolor{w h i t e}{.} l b$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Thus the raisins weight is $60 - 20 = 40 \textcolor{w h i t e}{.} l b$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Check: (40/60xx$3)+(20/60xx$6) =$4#