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You have $4.10 in nickels, dimes, and quarters. If you have twice as many dimes as quarters, and five more nickels than dimes, how many coins of each type do you have?

Respuesta :

carlosego

For this case, the first thing to do is define variables.

We have then:

  • x: number of nickels
  • y: number of dimes
  • z: number of quarters

We write now the system of equations:

[tex]0.05x + 0.1y + 0.25z = 4.10\\y = 2z\\x = y + 5[/tex]

Then rewriting the equations we have:

[tex]0.05 (2z + 5) + 0.1 (2z) + 0.25z = 4.1\\0.05 (2z + 5) + 0.1 (2z) + 0.25z = 4.1\\0.1z + 0.25 + 0.2z + 0.25z = 4.1\\0.55z = 4.1-0.25[/tex]

[tex]z = \frac {3.85} {0.55}\\z = 7[/tex]

Then, substituting values we have:

[tex]y = 2 (7)\\y = 14[/tex]

Finally:

[tex]x = 14 + 5\\x = 19[/tex]

Answer:

19 nickels

14 dimes

7 quarters

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