Question

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?

Answer 1

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

`" Oatmeal "=20^(lb)`

Explanation:

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

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)`