Question

One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 187.7 milligrams of vitamin C. Three eight-ounce glasses of apple juice and four eight-ounce glasses of

orange juice contain a total of 651.4 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

Answer 1

Answer: Let's use the following variables to represent the amount of vitamin C in an eight-ounce glass of each type of juice:

A: amount of vitamin C in an eight-ounce glass of apple juice (in milligrams)

O: amount of vitamin C in an eight-ounce glass of orange juice (in milligrams)

Using this, we can set up a system of two equations based on the given information:

Equation 1: A + O = 187.7 (total vitamin C in two glasses)

Equation 2: 3A + 4O = 651.4 (total vitamin C in three glasses of apple juice and four glasses of orange juice)

We can solve for one of the variables in terms of the other by rearranging Equation 1:

A = 187.7 - O

Substituting this expression for A into Equation 2, we get:

3(187.7 - O) + 4O = 651.4

Simplifying and solving for O, we get:

563.1 - 3O + 4O = 651.4

O = 88.3

Therefore, an eight-ounce glass of orange juice contains 88.3 milligrams of vitamin C. To find the amount of vitamin C in an eight-ounce glass of apple juice, we can substitute this value into Equation 1:

A + 88.3 = 187.7

A = 99.4

So, an eight-ounce glass of apple juice contains 99.4 milligrams of vitamin C.

Therefore, the amount of vitamin C in an eight-ounce glass of apple juice is 99.4 mg, and the amount of vitamin C in an eight-ounce glass of orange juice is 88.3 mg.

Explanation: