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.

IS IT D ?????

4 answers

Is it A?? @ms.sue

A should be correct.

Thank you.

To solve this problem, we can use a basic algebraic approach.

Let's assume the restaurant needs x gallons of the 12% lemonade and y gallons of the 7% lemonade to make 20 gallons of a 10% sugar mixture.

The total amount of sugar in x gallons of the 12% lemonade is 12x, and the total amount of sugar in y gallons of the 7% lemonade is 7y.

Since the total volume of the mixture is 20 gallons, we have the equation x + y = 20.

Since the desired sugar concentration in the mixture is 10%, the total amount of sugar in the mixture is 0.10 * 20 = 2.

Now we have a system of equations:

12x + 7y = 2 (equation 1)
x + y = 20 (equation 2)

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

Rearrange equation 2 to solve for x:
x = 20 - y

Substitute this expression for x in equation 1:
12(20 - y) + 7y = 2

Distribute the 12:
240 - 12y + 7y = 2

Combine like terms:
-5y + 240 = 2

Subtract 240 from both sides:
-5y = -238

Divide by -5:
y = 47.6

Since the question asks for gallons, we round up to the nearest whole number, which gives us y = 48.

Now substitute this value of y back into equation 2 to solve for x:
x + 48 = 20
x = -28

Since we cannot have negative amounts of lemonade, we discard the negative solution.

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