Solution:
Given:
Let the amount of Type 1 nitric acid used be represented by a
Let the amount of Type 2 nitric acid used be represented by b
Hence, the system of equations is;
[tex]\begin{gathered} Total\text{ }grams\text{ used is 42g} \\ a+b=42.................(1) \\ \\ \\ Cost\text{ of type 1 nitric acid is }0.45a \\ Cost\text{ of type 2 nitric acid is 0.30b} \\ Total\text{ cost of 42g used is \$14.40} \\ Hence, \\ 0.45a+0.30b=14.40...............(2) \end{gathered}[/tex]
Thus, solving the system of equations simultaneously,
From equation (1),
[tex]\begin{gathered} a=42-b \\ \\ Substitute\text{ into equation \lparen2\rparen} \\ 0.45(42-b)+0.3b=14.4 \\ 18.9-0.45b+0.3b=14.4 \\ 18.9-0.15b=14.4 \\ 18.9-14.4=0.15b \\ 4.5=0.15b \\ \\ Hence, \\ \frac{4.5}{0.15}=b \\ b=30 \end{gathered}[/tex]
Solving for a,
[tex]\begin{gathered} a=42-b \\ a=42-30 \\ a=12 \end{gathered}[/tex]
Therefore, the answer is;
12 grams of Type 1 and 30 grams of Type 2
