A 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. How many gallons of the 30% solution and 70%
solution should be mixed?
lion of the 30% solution should be mixed?

10 gallons of 30% solution and 30 gallons of 70% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of the 30% solution that should be mixed.

Let y represent the number of gallons of the 70% solution that should be mixed.

The total number of gallons of the mixture to be made is 40. This means that

x + y = 40

The 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 40 gallons of a 60% solution. This means that

0.3x + 0.7y = 0.6 × 40

0.3x + 0.7y = 24- - - - - - - - - - - - - -1

Substituting x = 40 - y into equation 1, it becomes

0.3(40 - y) + 0.7y = 24

12 - 0.3y + 0.7y = 24

- 0.3y + 0.7y = 24 - 12

0.4y = 12

y = 12/0.4

y = 30

x = 40 - y = 40 - 30

x = 10

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