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A combination of 20 coins, consisting of nickels and dimes, has a total monetary value of $1.55. Determine how many of each coin there are.

User Padma
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Final answer:

To determine how many nickels and dimes are in a combination of 20 coins with a total value of $1.55, you can set up a system of equations and solve for the variables. In this case, there are 9 nickels and 11 dimes in the combination of 20 coins.

Step-by-step explanation:

To determine how many nickels and dimes are in a combination of 20 coins with a total value of $1.55, we can set up a system of equations.

Let's assume the number of nickels is 'x' and the number of dimes is 'y'.

From the given information, we can create two equations:

  1. 5x + 10y = 155 (representing the total monetary value in cents)
  2. x + y = 20 (representing the total number of coins)

We can solve this system of equations using substitution or elimination. Let's use the elimination method:

  1. Multiply the second equation by 5 to make the coefficients of 'x' in both equations the same: 5x + 5y = 100
  2. Subtract equation 2 from equation 1 to eliminate 'x': (5x + 10y) - (5x + 5y) = 155 - 100
  3. Simplify the equation: 5y = 55
  4. Divide both sides by 5 to solve for 'y': y = 11
  5. Substitute the value of 'y' into equation 2 to solve for 'x': x + 11 = 20
  6. Solve for 'x': x = 9

Therefore, there are 9 nickels and 11 dimes in the combination of 20 coins.

User Piemonkey
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