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 find out how much of each mixture Kristen should combine, we can use a method called the "mixture problem." Here's how we can solve it step by step:

Step 1: Assign variables:
Let's say Kristen needs to mix x ounces of the 15% mixture and y ounces of the 30% mixture.

Step 2: Set up equations:
Since Kristen wants to make a total of 7.5 ounces of a 25% mixture, we can set up the following equations:

Equation 1: The total amount of mixture is 7.5 ounces.
x + y = 7.5

Equation 2: The total amount of jasmine in the mixture is 25% of 7.5 ounces.
0.15x + 0.30y = 0.25(7.5)

Step 3: Solve the system of equations:
We have two equations with two variables, so we can solve them simultaneously. Let's rearrange equation 2 to make it easier to solve:

0.15x + 0.30y = 0.25(7.5)
0.15x + 0.30y = 1.875

Multiply equation 1 by 0.15 to make the coefficients of x in both equations equal:

0.15x + 0.15y = 0.15(7.5)
0.15x + 0.15y = 1.125

Now, subtract this equation from the rearranged equation 2:
(0.15x + 0.30y) - (0.15x + 0.15y) = 1.875 - 1.125
0.30y - 0.15y = 0.75
0.15y = 0.75
y = 0.75 / 0.15
y = 5

Now substitute the value of y into equation 1 to find x:

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

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

To solve this problem, we can use a system of linear equations. Let's assume Kristen needs x ounces of the 15% jasmine mixture and y ounces of the 30% jasmine mixture to make a total of 7.5 ounces of the 25% jasmine essential oil.

We can set up the following equations based on the amount of jasmine oil in each mixture:

Equation 1: Amount of jasmine oil in the 15% mixture: 0.15x
Equation 2: Amount of jasmine oil in the 30% mixture: 0.30y

Equation 3: Total amount of jasmine oil in the 7.5 ounces of 25% mixture: 0.25(7.5) = 1.875

Since Kristen wants to make a total of 7.5 ounces of the 25% jasmine mixture, we have the equation:

Equation 4: x + y = 7.5

Now, we have a system of equations:

0.15x + 0.30y = 1.875 (Equation 1)
x + y = 7.5 (Equation 4)

Let's solve the system of equations using substitution or elimination method:

Using the elimination method, we can multiply Equation 4 by 0.15 (to make the coefficients of x match):

0.15(x + y) = 0.15(7.5)
0.15x + 0.15y = 1.125 (Equation 5)

Now, subtract Equation 5 from Equation 1:

0.15x + 0.30y - (0.15x + 0.15y) = 1.875 - 1.125
0.15x - 0.15x + 0.30y - 0.15y = 0.75
0.15y = 0.75
y = 0.75 / 0.15
y = 5

Substituting the value of y into Equation 4:

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

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

let the amount of the 15% mixture be x ounces

then the amount of the 30% mix is 7.5-x

.15x + .30(7.5-x) = .25(7.5)
times 100

15x + 30(7.5-x) = 25(7.5)
15x + 225 - 30x = 187.5
-15x = -37.5
x = 2.5

Use 2.5 ounces of the 15% mix and
5 ounces of the 30% mix