Let

x = no. of litres of pure gasoline

y = no. of litres of 5% gasoline

z = no. of litres of 6% gasoline

From the first sentence, we have:

x + y + z = 10

The second sentence gives us:

We get NO additive from the pure gasoline.

We get (5% of y) L of additive from the second drum.

We get (6% of z) L of additive from the third drum.

We NEED 2% of 10 L of additive = 0.2 L = 200 mL.

So

0.05y + 0.06z = 0.2

Multiplying through by 100 gives us:

5y + 6z = 20

The second last sentence gives us:

x = 4y

We can write this as:

x - 4y = 0

This gives us the set of simultaneous equations:

x + y + z = 10

5y + 6z = 20

x - 4y = 0

 

So

math expressionmath expression

 

Using Scientific Notebook for the inverse:

math expression

Multiplying the inverse by matrix C:

math expression

So we have 6.4 L of pure gasoline, 1.6 L of 5% additive and 2 L of 6% additive.

Is it correct?

6.4 + 1.6 + 2 = 10 L math expression

5% of 1.6 + 6% of 2 = 200 mL math expression

4 × 1.6 = 6.4 math expression