A commercial customer has ordered 104 gallons of paint that

A commercial customer has ordered 104 gallons of paint that contains an equal amount of red paint, yellow paint, green paint, and blue paint, and hence could be prepared by mixing 26 gallons of each color. However, the store wishes to prepare this order by mixing four types of paint that are already available in large quantity: Paint A is a mixture of 50.5% red, 9.5% yellow, 20% green, and 20% blue paint; Paint B is a mixture of 10% red, 2.5% yellow, 70% green, and 17.5% blue paint; Paint C is a mixture of 5% red, 20% yellow, 15% green, and 60% blue; and Paint D is a mixture of 15.5% red, 65.5% yellow, 4% green, and 15% blue. How many gallons of paints A, B, C, D are needed to prepare the customer\'s order? Write out a system of equations that represents the information given, then solve that system using Maple, Matlab, Wolfram alpha, or any other favorite mathematical software.

Solution

Let
red=x1
yellow=x2
green=x3
blue=x4

A=x5
B=x6
C=x7
D=x8

then we get equations:
x5+x6+x7+x8=104
x5=0.505x1+ 0.095x2+ 0.2x3+ 0.2x4
x6=0.1x1+ 0.025x2+ 0.7x3+ 0.175x4
x7=0.05x1+ 0.2x2+ 0.15x3+ 0.6x4
x8=0.155x1+ 0.655x2+ 0.04x3+ 0.15x4

now you can solve them by any of the software or program as listed below.