Answer: hi
We can begin by using algebra to represent the number of coins of each denomination. Let x be the number of pennies and dimes, and y be the number of quarters. Since there are equal number of pennies and dimes, we can write:
x + x + y = 56 (number of coins)
Next, we can use the information about the total value of the coins to set up another equation. We know that the total value is $6.59, and the value of each coin is:
Pennies: $0.01 * x = $0.01x
Dimes: $0.1 * x = $0.1x
Quarters: $0.25 * y = $0.25y
The total value is the sum of the value of each coin:
$0.01x + $0.1x + $0.25y = $6.59
Now we have a system of equations:
x + x + y = 56 and 0.01x + 0.1x + 0.25y = 6.59
We can now solve this system of equations using substitution method.
x + x + y = 56
x = 56 - y
Now we can substitute x in the second equation:
0.01(56-y) + 0.1(56-y) + 0.25y = 6.59
0.56 - 0.01y + 0.56 - 0.1y + 0.25y = 6.59
1.12 - 0.11y = 6.59
-0.11y = -5.47
y = 50
Now that we know the number of quarters, we can substitute it back into the equation x + x + y = 56
x = 6
So Carlos has 6 pennies and dimes, and 50 quarters in the box.
We can check this by multiplying the number of coins by their value and adding up
60.01 + 60.1 + 50*0.25 = 0.06 + 0.6 + 12.5 = 6.59
Explanation: