Answer:
B. 110
Explanation:
In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?
A. 90
B. 110
C. 130
D. 180
Answer:
Let x represent the amount of calories in 1 servings of juice, y represent the amount of calories in 1 servings of milk and z represent the amount of calories in 1 servings of Soda.
Joe consumption can be represented by:
x + 2y + z = 530 (1)
Darius consumption can be represented by:
2x + y = 370 (2)
Marian consumption can be represented by:
3y + z = 510 (3)
The equations can be represented in matrix form as:
![\left[\begin{array}{ccc}1&2&1\\2&1&0\\0&3&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}530\\370\\510\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&2&1\\2&1&0\\0&3&1\end{array}\right] ^(-1)\left[\begin{array}{c}530\\370\\510\end{array}\right] \\\\\\](https://img.qammunity.org/2021/formulas/mathematics/college/ify6ld8lwqwpx0ss6a0uzpau0sra2e8q16.png)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0.33&0.33&-0.33\\-0.67&0.33&0.67\\2&-1&-1\end{array}\right]\left[\begin{array}{c}530\\370\\510\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}130\\110\\180\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/m4imqhvv2t4q8r7a0njbk1pzuhgvh9d209.png)
The amount of calories in one serving of milk is 110 calories