Mathman couldn't resist the grooving tunes inside and paid his $5.00. He was heading straight for the punch bowl when he noticed a witch mixing it together using a solution which was 60% lizard drool and another that was only 25% lizard drool. If she wanted to make 30 liters of 39% lizard drool, how much of each does she need?

Question

Mathman couldn't resist the grooving tunes inside and paid his $5.00. He was heading straight for the punch bowl when he noticed a witch mixing it together using a solution which was 60% lizard drool and another that was only 25% lizard drool. If she wanted to make 30 liters of 39% lizard drool, how much of each does she need?

thanks so much!

Answer 1

Add up the amount of drool in each part.

.60x + .25(30-x) = .39*30
.60x + 7.5 - .25x = 11.7
.35x = 4.2
x = 12

12L 60%
18L 25%

Answer 2

To find out how much of each solution the witch needs, we can set up a system of equations. Let's first assign variables to represent the unknown quantities.

Let x represent the amount (in liters) of the 60% lizard drool solution.
Let y represent the amount (in liters) of the 25% lizard drool solution.

Now, we can set up two equations based on the given information:

Equation 1: The total volume of the solution is 30 liters.
x + y = 30

Equation 2: The resulting solution should be 39% lizard drool.
(0.60x + 0.25y) / 30 = 0.39

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

Step 1: Solve Equation 1 for x.
x = 30 - y

Step 2: Substitute the value of x from Step 1 into Equation 2.
(0.60(30 - y) + 0.25y) / 30 = 0.39

Step 3: Simplify and solve for y.

(18 - 0.60y + 0.25y) / 30 = 0.39
(18 - 0.35y) / 30 = 0.39
18 - 0.35y = 0.39 * 30
18 - 0.35y = 11.7
-0.35y = -6.3
y = (-6.3) / (-0.35)
y ≈ 18

Step 4: Substitute the value of y into Equation 1 to find x.
x + 18 = 30
x = 30 - 18
x = 12

So, the witch needs 12 liters of the 60% lizard drool solution and 18 liters of the 25% lizard drool solution to make 30 liters of the desired 39% lizard drool solution.