a restaurant has lemonade that is 12% sugar and another that is 7% sugar. How many gallons of each type does the restaurant need to make 20 gallons of a lemonade mixture that is 10% sugar.
A.) 12 gallons of 12% and 8 gallons of 7%
B.) 10 gallons of 12% and 10 gallons of 7%
C.) 8 gallons of 12% and 12 gallons of 7%
D.) 2gallons of 12% and 18 gallons of 7%
please help.
if anyone took connections im in Algebra 1 unit 7 lesson 8 if you could help
(x * .12) + [(20 - x) * .07] = 20 * .10
what does that mean
x is the number of gallons of 12%
you should be worried...
yep... i am so not ready for this. to to go and study AGAIN
To solve this problem, we can use a system of equations. Let's assume that the number of gallons of the 12% sugar lemonade is represented by "x", and the number of gallons of the 7% sugar lemonade is represented by "y".
From the problem statement, we know that the total volume of the lemonade mixture is 20 gallons. Therefore, we have the equation:
x + y = 20 (Equation 1)
We also know that the sugar content of the mixture is 10%. To find the sugar content, we need to consider the total amount of sugar from each type of lemonade.
For the 12% sugar lemonade, we have 0.12x gallons of sugar.
For the 7% sugar lemonade, we have 0.07y gallons of sugar.
We want the sugar content of the mixture to be 10%, so we set up the equation:
(0.12x + 0.07y)/(x + y) = 0.10 (Equation 2)
Now, we have a system of equations:
x + y = 20 (Equation 1)
(0.12x + 0.07y)/(x + y) = 0.10 (Equation 2)
To solve this system of equations, we can use substitution, elimination, or any other method taught in your Algebra 1 lesson.
Simplifying Equation 2, we get:
0.12x + 0.07y = 0.10(x + y)
0.12x + 0.07y = 0.10x + 0.10y
Rearranging terms, we have:
0.12x - 0.10x = 0.10y - 0.07y
0.02x = 0.03y
2x = 3y (Equation 3)
Now, we can substitute Equation 3 into Equation 1 to solve for x:
2x = 3y
2x = 3(20 - x)
2x = 60 - 3x
5x = 60
x = 12
Substituting the value of x back into Equation 1, we can solve for y:
12 + y = 20
y = 8
Therefore, the restaurant needs 12 gallons of the 12% sugar lemonade and 8 gallons of the 7% sugar lemonade to make 20 gallons of a lemonade mixture that is 10% sugar.
So, the answer is A.) 12 gallons of 12% and 8 gallons of 7%.