Question

Natalie kept track of her calcium intake from three sources for 3 days. The first day she had 3 glasses of milk, 4 servings of ice cream, and 1 calcium supplement in pill form which totaled 1680 mg of calcium. The second day she had 4 glasses of milk, 4 servings of ice cream, and 1 calcium supplement totaling 1880mg. The third day she had 3 glasses of milk, 5 servings of ice cream, and 1 calcium supplement for a total of 1750mg . Find the amount of calcium in one glass of milk, in one serving of ice cream, and in one calcium supplement.

Answer 1

The amount of calcium in one glass of milk is 200 mg, in one serving of ice cream is 70 mg and in one calcium supplement is 800 mg

Explanation:

We have the following:

Let x represent the amount of calcium in one glass of milk.

Let y represent the amount of calcium in one serving of ice cream.

Let z represent the amount of calcium in one calcium supplement.

To solve for three variables, we need to establish three independent relationships among x, y and z:

The first day she had 3 glasses of milk, 4 servings of ice cream, and 1 calcium supplement in pill form which totaled 1680 mg of calcium:

`3x+4y+z=1680`

The second day she had 4 glasses of milk, 4 servings of ice cream, and 1 calcium supplement totaling 1880 mg:

`4x+4y+z=1880`

The third day she had 3 glasses of milk, 5 servings of ice cream, and 1 calcium supplement for a total of 1750mg

`3x+5y+z=1750`

We solve the system of equations as follows (By substitution) :

`\begin{gathered} z=1680-3x-4y \\ \text{now, replacing} \\ 4x+4y+1680-3x-4y=1880 \\ x=1880-1680 \\ x=200 \end{gathered}`

now, for to calculate y:

`\begin{gathered} z=1680-3\cdot200-4y\rightarrow z=1080-4y \\ z=1750-3\cdot200-5y\rightarrow z=1150-5y \\ \text{ We equal and we have:} \\ 1080-4y=1150-5y \\ 5y-4y=1150-1080 \\ y=70 \end{gathered}`

Finally to calculate z:

`\begin{gathered} z=1680-3\cdot200-4\cdot70 \\ z=800 \end{gathered}`