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.

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SheliaJ102520 SheliaJ102520 · Answer 1 · 2022-11-03T06:23:08+01:00

Solution:

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

[tex]5x+4y=363[/tex]

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

This can be represented as

[tex]y=57[/tex]

Solving the equation, we have

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

Thus,

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