Question

enter the correct answer in the box.
suzie tutors and babysits after school and works at a grocery store on the weekends. she earns a different hourly wage for each of the three jobs: ( t ) dollars for tutoring, ( b ) dollars for babysitting, and ( g ) dollars for working at the grocery store.
the table shows the number of hours she worked at each job over the course of three weeks.

	week 1	week 2	week 3
babysitting	8	5	6
grocery store	6	4	4

in week 1, suzie earned $215; in week 2, she earned $145; and in week 3, she earned $170.
what matrix equation could be used to determine the hourly wage she earns for each job? fill in the missing elements in the equation.
\\( \

$$\begin{bmatrix} \\square & \\square & \\square \\\\ \\square & \\square & \\square \\\\ \\square & \\square & \\square \\end{bmatrix}$$

\

$$\begin{bmatrix} t \\\\ b \\\\ g \\end{bmatrix}$$

= \

$$\begin{bmatrix} \\square \\\\ \\square \\\\ \\square \\end{bmatrix}$$

\\) (matrix and equation input interface shown with various mathematical symbols and matrix boxes)

Explanation:

Step1: Define coefficient matrix

The coefficient matrix is formed by the number of hours worked each week for each job, ordered as Tutoring, Babysitting, Grocery Store:

$$\begin{bmatrix} 4 & 8 & 6 \\ 3 & 5 & 4 \\ 4 & 6 & 4 \end{bmatrix}$$

Step2: Define variable vector

The variable vector contains the hourly wages for each job:

$$\begin{bmatrix} t \\ b \\ g \end{bmatrix}$$

Step3: Define constant vector

The constant vector contains the total earnings each week:

$$\begin{bmatrix} 215 \\ 145 \\ 170 \end{bmatrix}$$

Step4: Assemble matrix equation

Combine the coefficient matrix, variable vector, and constant vector into a matrix equation where their product equals the constant vector.

Answer:

$$\begin{bmatrix} 4 & 8 & 6 \\ 3 & 5 & 4 \\ 4 & 6 & 4 \end{bmatrix}\begin{bmatrix} t \\ b \\ g \end{bmatrix}=\begin{bmatrix} 215 \\ 145 \\ 170 \end{bmatrix}$$