Sugar tooth Candi company needs 300 gallons of a 32% sucrose solution for a certain kind of candy. The company has a solution that is 60% sucrose and a solution that is 25% sucrose how many gallons of each should the company mix together to obtain the desired solution?

Let x be the number of gallons of the 60% sucrose solution.
Let y be the number of gallons of the 25% sucrose solution.

To obtain 300 gallons of a 32% sucrose solution, the following equation can be set up based on the amount of sugar in each solution:

0.60x + 0.25y = 0.32(300)

Now, we need to solve this system of equations to find the values of x and y.

Let's multiply the entire equation by 100 to eliminate the decimals:

60x + 25y = 32(300)

Simplifying further:

60x + 25y = 9600

To make the equation easier to work with, let's divide the entire equation by 5:

12x + 5y = 1920

Now, let's find two equations with opposite coefficients of x or y. We can multiply the second equation by 12 and the first equation by 5 to make the coefficients of x opposite:

60x + 25y = 9600 (Equation 1)
60x + 60y = 23040 (Equation 2)

Now, subtract Equation 1 from Equation 2 to eliminate the x variable:

(60x + 60y) - (60x + 25y) = 23040 - 9600

35y = 13440

To solve for y, divide both sides of the equation by 35:

y = 13440 / 35

Simplifying:

y = 384

Now, substitute the value of y back into Equation 1 and solve for x:

60x + 25(384) = 9600

60x + 9600 = 9600

60x = 0

x = 0

Therefore, to obtain 300 gallons of a 32% sucrose solution, Sugar tooth Candi company should mix 0 gallons of the 60% sucrose solution and 384 gallons of the 25% sucrose solution.

Answer: The company should mix 0 gallons of the 60% sucrose solution and 384 gallons of the 25% sucrose solution.