Question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.Tom and Gabrielle decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Tom went first and landed 5 arrows in the outer ring and 4 arrows in the bull's-eye, for a total of 363 points. Gabrielle went second and got 1 arrow in the bull's-eye, earning a total of 57 points. How many points is each region of the target worth?The outer ring is with ? points, and the bull’s eye is worth ? points.

Answer 1

Let the points awarded to outer ring region be represented with x

Let the points awarded to bull's eye region be represented with y

Given that

Tom went first and landed 5 arrows in the outer ring and 4 arrows in the bull's-eye, for a total of 363 points. This can be represented by

`5x+4y=363`

Gabrielle went second and got 1 arrow in the bull's-eye, earning a total of 57 points.

This can be represented as

`y=57`

Solving the equation, we have

`\begin{gathered} 5x+4y=363 \\ y=57 \\ \\ 5x+4(57)=363 \\ 5x+228=363 \\ 5x=363-228 \\ 5x=135 \\ x=(135)/(5) \\ x=27 \end{gathered}`

Thus,

The outer ring is worth 27 points, and the bull’s eye is worth 57 points.