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

`A=((1,1,1),(0,5,6),(1,-4,0))`, `\ C=((10),(20),(0))`

Using Scientific Notebook for the inverse:

`((1,1,1),(0,5,6),(1,-4,0))^-1` `=((0.96,-0.16,0.04),(0.24,-0.04,-0.24),(-0.2,0.2,0.2))`

Multiplying the inverse by matrix C:

`((0.96,-0.16,0.04),(0.24,-0.04,-0.24),(-0.2,0.2,0.2))((10),(20),(0))` `=((6.4),(1.6),(2))`

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 [Checks OK]

`5% xx 1.6 + 6% xx 2 = 200` mL [Checks OK]

`4 × 1.6 = 6.4` [Checks OK]