Answer:
P = 51.0 L Blue + 173.2 L UV
Q = 338.9 L Blue + 369.8 L UV
Explanation:
Each litre of blue colour contains 0.14 L P and 0.407 L Q.
Each litre of UV agent contains 0.475 L P and 0.444 L Q.
You have 390 L blue colour and 543 L of UV agent and must make the maximum amount of P and Q.
This gives you two simultaneous equations:
[tex]\begin{array}{rcl}(1) &0.14P + 0.407Q & =& 390 \\(2) &0.475P + 0.444Q &=&543 \\\end{array}[/tex]
1. Calculate P and Q
[tex]\begin{array}{lrcll}(1) & 0.14P + 0.407Q & =& 390 & \\(2) & 0.475P + 0.444Q &=&543 & \\(3) & 0.0665P + 0.1933Q& = & 185.2 &\text{Multiplied (1) by 0.475} \\(4) & 0.0665P + 0.062 16Q &= & 76.02 & \text{Multiplied (2) by 0.14}\\(5) & 0.1312Q & = & 109.2 & \text{Subtracted (4) from (3)}\\\end{array}\[/tex]
[tex]\begin{array}{lrcll}(6)& Q & = & \mathbf{832.8} &\text{Divided each side by 0.1312} \\& 0.14P + 338.9 & =& 390 & \text{Substituted(6) into (1)}\\& 0.14P & =& 390 & \text{Subtracted 338.9 from each side}\\& P & =& \mathbf{364.7}&\text{Divided each side by 0.14} \\\end{array}[/tex]
P = 364.7 L and Q = 832.8 L
2. Composition of P and Q
P will contain
0.14 × 364.7 L Blue + 0.475 × 364.7 L UV = 51.0 L Blue + 173.2 L UV
Q will contain
0.407 × 832.8 L Blue + 0.444 × 832.8 L UV = 338.9 L Blue + 369.8 L UV
