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anna has 80coins of 5 cents and 20 cents values. In total they have a value of $10.45. How many of each does Anna have?

Question

anna has 80coins of 5 cents and 20 cents values. In total they have a value of $10.45. How many of each does Anna have?

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Solution

Let's denote:

  • the number of 5 cent coins as x
  • the number of 20 cent coins as y

From the problem, we have two equations:

  1. x + y = 80 (since the total number of coins is 80)
  2. 0.05x + 0.20y = 10.45 (since the total value of the coins is $10.45)

We can solve this system of equations step by step:

Step 1: Multiply the first equation by 0.05 to make the coefficients of x in both equations the same:

0.05x + 0.05y = 4

Step 2: Subtract the new equation from the second equation:

0.05x + 0.20y - (0.05x + 0.05y) = 10.45 - 4

This simplifies to:

0.15y = 6.45

Step 3: Solve for y by dividing both sides of the equation by 0.15:

y = 6.45 / 0.15 = 43

Step 4: Substitute y = 43 into the first equation:

x + 43 = 80

Solve for x:

x = 80 - 43 = 37

So, Anna has 37 coins of 5 cents and 43 coins of 20 cents.

This problem has been solved

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