One type of anyifreeze is 40% glycol, and another type of antifreeze is 60% glycol. How much of each kind should be used to make 100 gallons of antifreeze that is 48% glycol? How do i show my work? Thanks

make sure that the amounts of glycol in each part add up to the total.

If there are x gal of 40%, then the rest (100-x) is 60%, so we have

.40x + .60(100-x) = .48(100)

To solve this problem, we need to set up a system of equations using the information provided and solve for the unknown quantities. Let's denote the volume of the first type of antifreeze (40% glycol) as "x" gallons, and the volume of the second type of antifreeze (60% glycol) as "y" gallons.

First, let's establish the equation for the overall glycol content in the mixture. Since we want to end up with 100 gallons of antifreeze that is 48% glycol, we can write:

0.40x + 0.60y = 0.48 * 100

Simplifying the equation, we have:

0.40x + 0.60y = 48

Now, we need to incorporate the volume constraint that the total amount of antifreeze used is 100 gallons:

x + y = 100

So we have a system of two equations:

0.40x + 0.60y = 48 (Equation 1)
x + y = 100 (Equation 2)

To solve this system, we can use either substitution or elimination method. In this case, let's solve it using substitution.

Rearrange Equation 2 to solve for x:

x = 100 - y

Now substitute this equation for x in Equation 1:

0.40(100 - y) + 0.60y = 48

We can now solve this equation for y:

40 - 0.40y + 0.60y = 48
0.20y = 48 - 40
0.20y = 8
y = 8 / 0.20
y = 40

Now that we know y = 40, we can substitute this value back into Equation 2 to solve for x:

x + 40 = 100
x = 100 - 40
x = 60

Therefore, you need to use 60 gallons of the 40% glycol antifreeze and 40 gallons of the 60% glycol antifreeze to make 100 gallons of a 48% glycol antifreeze mixture.

To show your work, you would write:

Let x = volume (in gallons) of 40% glycol antifreeze.
Let y = volume (in gallons) of 60% glycol antifreeze.

Equation 1: 0.40x + 0.60y = 48
Equation 2: x + y = 100

Solving the system of equations, we find x = 60 gallons and y = 40 gallons.