daigo said:
The equation is: 0.01x + 0.05y + 0.10z = 1.54, where x is the number of pennies, y is the number of nickels, and z is the number of dimes.
Since we know that Bobbie has a total of $1.54 in coins, we can set up the equation as 0.01x + 0.05y + 0.10z = 1.54. We also know that the total number of coins is 100 (x + y + z = 100).
We can use the substitution method to solve the equation. First, we can solve for one variable (e.g. z) in terms of the other two variables (x and y). Then, we can substitute the value of z into the original equation and solve for the remaining two variables. Finally, we can plug in the values of x and y into the total number of coins equation to find the number of each type of coin.
To check your solution, you can plug in the values for x, y, and z into the original equation. If the equation is true, then your solution is correct. You can also check by adding up the total value of each type of coin (e.g. 0.01x + 0.05y + 0.10z) and making sure it equals $1.54.
After solving the algebraic equation, the final answer is: Bobbie has 44 pennies, 10 nickels, and 46 dimes in her coin collection.