How many ml needs to be mixed?

Question

A scientist needs 120 ml of a 70% solution to be made from a mixture of 60% and 80% solutions. How many ml of each should be mixed to get the needed solution?

Answer 1

X+Y = 120

X= 120-Y

60X + 80Y = 70(120)

6X + 8Y = 7(120)

3X + 4Y = 7(60) = 420

3(120-Y) + 4Y = 420

360-3Y +4Y = 420

Y = 420-360 = 60 ml of 60% solution

X= 120-60 = 60 ml of 80% solution

Actually you could have seen that from the beginning, without any real calculations or algebra, as 70 is the midpoint between 60 and 80, so you'd need equal amounts of each solution or 120/2 = 60 for each.