Question

Jerry tries to exercise each day of the week. He burns 850 calories when he runs and 200 calories when he lifts weights. Last week he exercised for a total of 6.5 hours and burn 2,925 total calories. How long does he spend on each exercise? Which augmented matrix can be used to represent the system of equations used to solve the problem above?

Answer 1

Case: Augmented Matrix

Given:

In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.

Given:

He burns 850 calories when he runs.

he burns 200 calories when he lifts weight

he exercised for a total of 6.5 hours

he burns 2,925 total calories

Method:

First, we make a linear equation:

Assumption: Let the number of hours he runs be r. The number of hours he lifts weights be w.

The equation therefore is:

Hours:

r + w = 6.5

Calories:

850x + 200y = 2925

Final answer:

Augmented Matrix

`\begin{bmatrix}{1} & {1} & 6.5 \\ {850} & {200} & 2925 \\ {} & {} & {}\end{bmatrix}`