Final answer:
Kitara has 60 quarters and 40 dimes, which can be determined by setting up a system of equations based on the total number of coins and their combined value.
Step-by-step explanation:
The question asks us to determine how many quarters and dimes Kitara has, given that she has 100 coins in total and that they have a combined value of $19. To solve this, we can set up a system of equations. Let's denote the number of quarters as Q and the number of dimes as D. The first equation comes from the total number of coins: Q + D = 100. The second equation comes from the total value of the coins (in cents): 25Q + 10D = 1900 (since $19 is equivalent to 1900 cents).
Solving this system of equations, we subtract the second equation (in its dime-equivalent form, i.e. dividing by 10) from the first: Q + D = 100 and 2.5Q + D = 190, which after subtraction gives us 1.5Q = 90, or Q = 60. Therefore, Kitara has 60 quarters. Using the first equation, D = 100 - 60, which means Kitara has 40 dimes.