Question #9c89b

2 Answers
May 30, 2017

Answer:

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

Explanation:

Let nuts combined is #x# lb , then raisin combined is #(60-x)# 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#

#:. 3x+180 = 240 or 3x =60 or x=20 :. 60-x=60-20=40#

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

May 30, 2017

Answer:

#color(blue)("A different method.")#

Raisons #->40color(white)(.)lb#
Nuts #" "->20color(white)(.)lb#

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.

Tony B

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:

#(ncolor(white)(.)lb)/(4-3)=(60color(white)(.)lb)/(6-3)#

#n=(60color(white)(.)lb)/3=20color(white)(.)lb#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus the raisins weight is #60-20=40color(white)(.)lb#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:

#(40/60xx$3)+(20/60xx$6) =$4#