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At an archery competition, Jamie and Marshall's team tied Shawna and Wyatt's team for the top team score. Team scores are determined by adding the two teams members individual scores. Marshall scores 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored 4 less than Shawna. What was each person's individual score?

Respuesta :

Given:

Jamie and Marshall's team tied Shawna and Wyatt's team for the top team score.

Marshall scores 12 less than Jamie. Shawna scored twice as much as Marshall. Wyatt scored 4 less than Shawna.

To find:

The individual score of each person.

Solution:

Let x be the score of Jamie.

Marshall scores 12 less than Jamie.

Marshall score = x-12

Shawna scored twice as much as Marshall.

Shawna score = 2(x-12)

Wyatt scored 4 less than Shawna.

Wyatt score = 2(x-12)-4

Now,

Score of Jamie and Marshall's team [tex]=x+(x-12)[/tex]

Score of Shawna and Wyatt's team [tex]=2(x-12)+2(x-12)-4[/tex]

Jamie and Marshall's team tied Shawna and Wyatt's team

[tex]x+(x-12)=2(x-12)+2(x-12)-4[/tex]

[tex]x+x-12=2x-24+2x-24-4[/tex]

[tex]2x-12=4x-52[/tex]

Isolate x.

[tex]2x-4x=-52+12[/tex]

[tex]-2x=-40[/tex]

Divide both sides by -2.

[tex]x=\dfrac{-40}{-2}[/tex]

[tex]x=20[/tex]

So, Jamie score = 20

Marshall score = 20-12

                        = 8

Shawna score = 2(20-12)

                        = 2(8)

                        = 16

Wyatt score = 2(20-12)-4

                     = 2(8)-4

                     = 16-4

                     = 12

Therefore, the scores of Jamie, Marshall, Shawna and Wyatt are 20, 8, 16 and 12 respectively.

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