Question

The cost of 42 grams of a nitric acid is $14.40. Type 1 nitric acid costs 45€ a gramtype 2 nitric acid costs 30¢ a gram. How many grams of each nitric acid were usecform the compound?

Answer 1

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;

`\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}`

Thus, solving the system of equations simultaneously,

From equation (1),

`\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, \\ (4.5)/(0.15)=b \\ b=30 \end{gathered}`

Solving for a,

`\begin{gathered} a=42-b \\ a=42-30 \\ a=12 \end{gathered}`

Therefore, the answer is;

12 grams of Type 1 and 30 grams of Type 2