One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 180 milligrams of vitamin C. Four eight-ounce glasses of apple juice and three eight-ounce glasses of orange juice contain a total of 637.4 milligrams of vitamin C. How much vitamin C is in an eight-ounce glass of each type of juice?
apple juice ___ mg
orange juice __ mg
just turn all those words into algebra:
If there are
x mg of vitamin C in a glass of apple juice
y mg in a glass of orange juice
then consider the amount of vitamin C as described above:
x+y = 180
4x+3y = 637.4
now just find x and y
It could have been worse; the glasses might have been of different sizes!
Helped a lot thank you
12
To find out how much vitamin C is in an eight-ounce glass of each type of juice, we can set up a system of equations.
Let's assign variables to represent the unknown quantities:
- Let A be the amount of vitamin C in an eight-ounce glass of apple juice.
- Let O be the amount of vitamin C in an eight-ounce glass of orange juice.
We can now translate the given information into two equations:
Equation 1: One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 180 milligrams of vitamin C.
A + O = 180
Equation 2: Four eight-ounce glasses of apple juice and three eight-ounce glasses of orange juice contain a total of 637.4 milligrams of vitamin C.
4A + 3O = 637.4
Now we can solve this system of equations to find the values of A and O.
There are several methods to solve a system of equations, such as substitution or elimination. Let's use the substitution method here:
Step 1: Solve Equation 1 for A:
A = 180 - O
Step 2: Substitute the value of A in Equation 2 with 180 - O:
4(180 - O) + 3O = 637.4
Step 3: Simplify and solve for O:
720 - 4O + 3O = 637.4
720 - O = 637.4
-O = 637.4 - 720
-O = -82.6
O = 82.6
Step 4: Substitute the value of O back into Equation 1 to solve for A:
A + 82.6 = 180
A = 180 - 82.6
A = 97.4
Therefore, an eight-ounce glass of apple juice contains 97.4 milligrams of vitamin C, and an eight-ounce glass of orange juice contains 82.6 milligrams of vitamin C.