# 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 Jul 3, 2016 $\text{ Bran flakes } = {10}^{l b}$$\text{ Oatmeal } = {20}^{l b}$#### 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"
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The final mix is to have the weight of ${30}^{l b}$

$\implies \text{ Bran flakes } = \frac{33 \frac{1}{3}}{100} \times 30 = {10}^{l b}$

$\implies \text{ Oatmeal } = 30 - 10 = {20}^{l b}$