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 x
\begin{align*} 5x + 4y &= 265 \quad \text{(Darrell's score)} \\ 5x + 2y &= 165 \quad \text{(Zoe's score)} \end{align*}
To solve this system, we can use the elimination method. We can subtract the second equation from the first equation to eliminate x
(5x + 4y) - (5x + 2y) = 265 - 165
Simplifying the equation, we get:
2y = 100
Dividing both sides by 2, we find:
y = 50
Now that we have the value of y
5x + 2(50) = 165
Simplifying the equation, we get:
5x + 100 = 165
Subtracting 100 from both sides, we have:
5x = 65
Dividing both sides by 5, we find:
x = 13
Therefore, the outer ring is worth \boxed{13}
and the points for the bull's-eye as y
. We can set up the following system of equations based on the information provided:
\begin{align*} 5x + 4y &= 265 \quad \text{(Darrell's score)} \\ 5x + 2y &= 165 \quad \text{(Zoe's score)} \end{align*}
To solve this system, we can use the elimination method. We can subtract the second equation from the first equation to eliminate x
:
(5x + 4y) - (5x + 2y) = 265 - 165
Simplifying the equation, we get:
2y = 100
Dividing both sides by 2, we find:
y = 50
Now that we have the value of y
, we can substitute it back into one of the original equations to solve for x
. Let's use the second equation:
5x + 2(50) = 165
Simplifying the equation, we get:
5x + 100 = 165
Subtracting 100 from both sides, we have:
5x = 65
Dividing both sides by 5, we find:
x = 13
Therefore, the outer ring is worth \boxed{13}
points, and the bull's-eye is worth \boxed{50}
points.
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