A health food store sells oatmeal for $3.60 per pound and bran flakes for $4.80 per pound. How many pounds of each should be used to get a mixture of 30 pounds that sells for $4.00 a pound?

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Answer 1 · 2016-07-03T20:30:54

#" Bran flakes " = 10^(lb)#

#" Oatmeal "=20^(lb)#

Basically this is a straight line graph Plotting cost against content of Bran Flakes.

Tony B

At 0% Bran Flakes the mix is 100% Oatmeal
At 100% Bran Flakes the mix is 0% Oatmeal

Gradient is #($4.80-$3.60)/(100%) =($1.20)/(100%)#

The gradient of part of the graph is the same as the gradient of all of the graph.

So #($4.00-$3.60)/(x%)=($4.80-$3.60)/(100%)#

# ($1.20)/(100%)=($0.40)/(x%)#

Turning the whole thing upside down

#(100%)/1.2=(x%)/0.4#

Multiply both sides by #0.4#

#x%=(0.4xx100)/(1.2)= 33.333bar3 = 33 1/3%" bran flakes"#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The final mix is to have the weight of #30^(lb)#

#=>" Bran flakes "= (33 1/3)/100xx30 = 10^(lb)#

#=>" Oatmeal "= 30-10=20^(lb)#