Kristen wants to make 7.5 ounces of a 25% jasmine essential oil. She only has a 15% jasmine mixture and a 30% jasmine mixture available. How much of each mixture should she combine to create the desired oil?

To determine how much of each mixture Kristen should combine, we can set up an equation based on the given information.

Let's assume Kristen uses x ounces of the 15% jasmine mixture and y ounces of the 30% jasmine mixture.

The total amount of jasmine mixture created will be x + y ounces.

The equation to represent the total amount of jasmine in the new mixture is:

0.15x + 0.30y = 0.25 * 7.5

Let's simplify the equation:

0.15x + 0.30y = 1.875

To solve the equation, we need another equation to represent the total amount of the mixture. We know that x + y = 7.5 since Kristen wants to make 7.5 ounces of the essential oil.

Now we have a system of equations:

0.15x + 0.30y = 1.875
x + y = 7.5

We can solve this system of equations using substitution or elimination method. Let's solve it using substitution.

Rearrange the second equation: x = 7.5 - y

Substitute this value of x into the first equation:

0.15(7.5 - y) + 0.30y = 1.875

Multiply through:

1.125 - 0.15y + 0.30y = 1.875

Combine like terms:

0.15y = 1.875 - 1.125
0.15y = 0.750

Divide both sides by 0.15:

y = 0.750 / 0.15
y = 5

Now substitute this value of y back into the second equation to find x:

x + 5 = 7.5
x = 7.5 - 5
x = 2.5

Therefore, Kristen should combine 2.5 ounces of the 15% jasmine mixture with 5 ounces of the 30% jasmine mixture to create 7.5 ounces of the desired 25% jasmine essential oil.