A restaurant has one type of lemonade that has 12% sugar and another that is 7% sugar. How many gallons of each does the restaurant need to make 20 gallons of a lemonade mixture that is 10% sugar?

a. 12 gallons of the 12% lemonade and 8 gallons of the 7% lemonade.

b.10 gallons of the 12% lemonade and 10 gallons of the 7% lemonade.

c.8 gallons of the 12% lemonade and 12 gallons of the 7% lemonade.

d.2 gallons of the 12% lemonade and 18 gallons of the 7% lemonade. *****

I change my answer to A

Yes, A is correct.

Thank you!

To solve this problem, we can set up a system of equations using the concept of mixtures.

Let's say x represents the gallons of the 12% lemonade and y represents the gallons of the 7% lemonade.

The first equation represents the total amount of lemonade: x + y = 20 (since we need to make 20 gallons in total)

The second equation represents the sugar content in the mixture: (0.12x + 0.07y)/20 = 0.10

To solve this system of equations, we can use substitution or elimination.

Using elimination, we can multiply the first equation by 0.12 to eliminate x:

0.12x + 0.12y = 2.4
0.12x + 0.07y = 2

Subtracting the second equation from the first, we get:
0.12y - 0.07y = 2.4 - 2
0.05y = 0.4
y = 0.4/0.05
y = 8

Now, substitute the value of y into the first equation to solve for x:
x + 8 = 20
x = 20 - 8
x = 12

So, the correct answer is d. 2 gallons of the 12% lemonade and 18 gallons of the 7% lemonade.