In mixing a weed killing chemical a 40% solution of the chemical is mixed with an 85% solution to get 20 L of a 60% solution. How much of each solution is needed?

Question

In mixing a weed killing chemical a 40% solution of the chemical is mixed with an 85% solution to get 20 L of a 60% solution. How much of each solution is needed?

Answer 1

If x at 40%, the rest (20-x) is 85%. So,

.40x + .85(20-x) = .60(20)

Answer 2

amount of 40% stuff --- x L

amount of 85% stuff --- 20-x L

.4x + .85(20-x) = .60x

Answer 3

go with Steve, I messed up, right side is .60(20)

Answer 4

Well, it seems like you're dealing with some mixed-up vegetation. But don't worry, I'll help you weed out the problem! Let's break it down:

Let's call the amount of the 40% solution you need to mix "x" liters. And since the total volume of the final solution is 20L, the amount of the 85% solution will be 20 - x liters.

Now, let's talk about the percentages. The desired solution is 60% concentration. That means, from our x liters of the 40% solution, we'll have 0.4x liters of pure weed killer. And from our (20 - x) liters of the 85% solution, we'll have 0.85(20 - x) liters of pure weed killer.

Adding these two amounts together should give us the desired concentration. So, let's set up the equation:

0.4x + 0.85(20 - x) = 0.6(20)

Now, let the math game begin!

Answer 5

To solve this problem, we will use the method of mixing solutions.

Let's first assign variables to the two unknown quantities in the problem. Let's say x represents the amount (in liters) of the 40% solution needed and y represents the amount (in liters) of the 85% solution needed.

Now, let's set up the equations based on the given information:

Equation 1: x + y = 20 (since we want a total volume of 20 liters)

Equation 2: (0.40x + 0.85y) / 20 = 0.60 (since we want a 60% solution)

Simplifying Equation 2:

0.40x + 0.85y = 0.60 * 20
0.40x + 0.85y = 12

Now we have a system of equations:

Equation 1: x + y = 20
Equation 2: 0.40x + 0.85y = 12

To solve this system, we can use the method of substitution or elimination. Let's solve it using the substitution method.

1. Solve Equation 1 for x:
x = 20 - y

2. Substitute x in Equation 2 with the value found from Equation 1:
0.40(20 - y) + 0.85y = 12
8 - 0.40y + 0.85y = 12
0.45y = 4
y = 4 / 0.45
y = 8.89 liters

3. Substitute the value of y back into Equation 1 to find x:
x = 20 - 8.89
x = 11.11 liters

So, to obtain a 20 L of a 60% solution, you would need 11.11 liters of the 40% solution and 8.89 liters of the 85% solution.