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?

1 Answer
Tony B
Jul 3, 2016

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

" Oatmeal "=20^(lb) Oatmeal =20lb

Explanation:

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%)$4.80−$3.60100%=$1.20100%

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%)$4.00−$3.60x%=$4.80−$3.60100%

($1.20)/(100%)=($0.40)/(x%)$1.20100%=$0.40x%

Turning the whole thing upside down

(100%)/1.2=(x%)/0.4100%1.2=x%0.4

Multiply both sides by 0.40.4

x%=(0.4xx100)/(1.2)= 33.333bar3 = 33 1/3%" bran flakes"x%=0.4×1001.2=33.333¯3=3313% bran flakes
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

=>" Bran flakes "= (33 1/3)/100xx30 = 10^(lb)⇒ Bran flakes =3313100×30=10lb

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

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