Pergunta

Write a system of equations to describe the situation below,solve using any method, and fill in the blanks. Darrell and Zoe decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye Darrell went first and landed 5 arrows in the outer ring and 4 arrows in the bull's-eye, for a total of 265 points. Zoe went second and got 5 arrows in the outer ring and 2 arrows in the bull's -eye, earning a total of 165 points How many points is each region of the target worth? The outer ring is worth square points, and the bull's-eye is worth square points.
Solução

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AuroraVeterano · Tutor por 10 anos
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Let's denote the points for the outer ring as
To solve this system, we can use the elimination method. We can subtract the second equation from the first equation to eliminate
Simplifying the equation, we get:
Dividing both sides by 2, we find:
Now that we have the value of
Simplifying the equation, we get:
Subtracting 100 from both sides, we have:
Dividing both sides by 5, we find:
Therefore, the outer ring is worth
and the points for the bull's-eye as
. We can set up the following system of equations based on the information provided:
To solve this system, we can use the elimination method. We can subtract the second equation from the first equation to eliminate
:
Simplifying the equation, we get:
Dividing both sides by 2, we find:
Now that we have the value of
, we can substitute it back into one of the original equations to solve for
. Let's use the second equation:
Simplifying the equation, we get:
Subtracting 100 from both sides, we have:
Dividing both sides by 5, we find:
Therefore, the outer ring is worth
points, and the bull's-eye is worth
points.
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