Let x=10% acid y=20% acid z=40% acid.

We know that the total volume of the solution should be 100 mL so

is the first equation

For the next one the percents multiplied by the volume used need to add up so we get

Note: I multiplied the above equation by 10 to eliminate the decimals.

For the last equation we know that he uses 4 times as much of 10% as 40%

note that the equation is not this is a common error.

We now have a system of three equations with three unknowns.

Good luck.