Question

You create a recipe for slime by mixing some 20% pure slime and some 80% pure slime to create 1000 gallons of a 65% pure slime mixture. How many gallons of the 20% mixture are needed?

Answer 1

We can start solving this problem by using a system of linear equations. Let x be the number of gallons of the 20% pure slime mixture and y be the number of gallons of the 80% pure slime mixture. We know the following:

The total amount of slime mixture is 1000 gallons. This means that x + y = 1000.

The final mixture is 65% pure slime, which means that 0.65 = (0.20)x + (0.80)y. This is because we are mixing 20% pure slime and 80% pure slime to get the final mixture.

We can use these two equations to solve for x, which is the number of gallons of the 20% pure slime mixture needed.

First, we'll use the first equation to solve for y in terms of x:

y = 1000 - x

Then we'll substitute this expression into the second equation:

0.65 = (0.20)x + (0.80)(1000 - x)

Simplifying we get:

0.65 = 0.20x + 800 - 0.80x

0.45x = 200

x = 200/0.45

x = 444.44 gallons

So, you would need 444.44 gallons of the 20% pure slime mixture to make 1000 gallons of a 65% pure slime mixture.

Explanation: