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Volgvan
3 years ago
6

You have $4.10 in nickels, dimes, and quarters. If you have twice as many dimes as quarters, and five more nickels than dimes, h

ow many coins of each type do you have?
Mathematics
1 answer:
lutik1710 [3]3 years ago
6 0

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

We have then:

  • <em>x: number of nickels </em>
  • <em>y: number of dimes </em>
  • <em>z: number of quarters </em>

We write now the system of equations:

0.05x + 0.1y + 0.25z = 4.10\\y = 2z\\x = y + 5

Then rewriting the equations we have:

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

z = \frac {3.85} {0.55}\\z = 7

Then, substituting values we have:

y = 2 (7)\\y = 14

Finally:

x = 14 + 5\\x = 19

Answer:

19 nickels

14 dimes

7 quarters

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