Answer to Question #328011 in Financial Math for Busi

Question

A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually

sells for R420,00 per kilogram. The cheaper brand sells for R180,00 per kilogram. How much of each type

should be mixed in order to have 30 kilograms of coffee that is worth R240,00 per kilogram?

Choose the correct sentence:

[1] Three quarters of the mass should be from the cheaper brand.

[2] He should order 7,50 kg of the cheaper brand.

[3] A third of the mass should be from the gourmet brand.

[4] He should order 6,14 kg of the gourmet brand.

Answer 1

$x_1\,\,gourmet\\x_2\,\,cheaper\\\left\{ \begin{array}{c} x_1+x_2=30\\ \frac{420x_1+180x_2}{30}=240\\\end{array} \right. \Rightarrow \left\{ \begin{array}{c} x_1+x_2=30\\ 7x_1+3x_2=120\\\end{array} \right. \Rightarrow \left\{ \begin{array}{c} x_2=30-x_1\\ 7x_1+90-3x_1=120\\\end{array} \right. \Rightarrow \\\Rightarrow x_1=7.5,x_2=22.5\\x_2=\frac{3}{4}\cdot 30\\\left[ 1 \right] \,\,is\,\,correct\\$