A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. How many gallons of the 20% solution and 50%
solution should be mixed?

60 gallons of the 20% solution and 120 gallons of the 50% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of 20% solution that should be mixed.

Let y represent the number of gallons of 50% solution that should be mixed.

A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. This means that

0.2x + 0.5y = 0.4×180

0.2x + 0.5y = 72- - - - - - - - - - - -1

Since the total number of gallons is 180, it means that

x + y = 180

Substituting x = 180 - y into equation 1, it becomes

0.2(180 - y) + 0.5y = 72

36 - 0.2y + 0.5y = 72

- 0.2y + 0.5y = 72 - 36

0.3y = 36

y = 36/0.3

y = 120

x = 180 - y = 180 - 120

x = 60