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jade mattew and zane collect stamps jade and mathew have 220 more than zane. zane amd matthew have 140 more than jade. jade and zane have 500 how many stamps does matthew have?

Respuesta :

Using a system of equations, it is found that Matthew has 180 stamps.

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  • This problem is solved using a system of equations.
  • Jade has x stamps.
  • Matthew has y stamps.
  • Zane has z stamps.

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Jade and Matthew have 220 more than Zane, thus:

[tex]x + y = z + 220[/tex]

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Zane and Matthew have 140 more than Jade, thus:

[tex]y + z = x + 140[/tex]

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Jade and Zane have 500, thus:

[tex]x + z = 500 \rightarrow z = 500 - x[/tex]

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Replacing the last equation into the first two:

[tex]x + y = z + 220[/tex]

[tex]x + y = 500 - x + 220[/tex]

[tex]2x + y = 720[/tex]

[tex]y + z = x + 140[/tex]

[tex]y + 500 - x = x + 140[/tex]

[tex]-2x + y = -360[/tex]

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Adding the two equations:

[tex]2x - 2x + y + y = 720 - 360[/tex]

[tex]2y = 360[/tex]

[tex]y = \frac{360}{2}[/tex]

[tex]y = 180[/tex]

Matthew has 180 stamps.

A similar problem is given at https://brainly.com/question/17096268

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