let 'x' be the amount with 70% alcohol
'y' be the amount with 40% alcohol
you're given that the resulting solution must be 60% concentrated and that the total amount would be 150ml. from there we can say that
x + y = 150 ------let this be equation 1
in getting the desired concentration, you'll have the equation as:
0.70x + 0.40y = 0.60(150) -----equation 2
from equation 1, we can get the value of x in terms of y
x + y = 150
x = 150 - y -----equation 3
substitute equation 3 to 2
0.70x + 0.40y = 0.60(150)
0.70(150 - y) + 0.40y = 90
105 - 0.70y + 0.40y = 90
-0.70y + 0.40y = 90 - 105
-0.30y = -15
y = 50ml
substituting the value of y in equation 3
x = 150 - y
x = 150 - 50
x = 100ml
