Final answer:
By setting up a system of equations and solving for the number of dimes (d) and quarters (q) Jessica has, we find that she has 14 dimes and 2 quarters. Whitney has twice as many dimes and the same number of quarters, totaling in the same amount of money.
Step-by-step explanation:
Jessica and Whitney each have a combination of dimes and quarters that total the same amount of money, with Jessica having 16 coins in total. Since we are dealing with the values of money and the number of coins, we can set up a system of equations to solve this problem.
First, let's define variables: let d be the number of dimes and q be the number of quarters Jessica has. It follows that Whitney has 2d dimes and q quarters.
Given that Jessica has 16 coins: d + q = 16 (Equation 1)
Since the value of a dime is 10 pennies and the value of a quarter is 25 pennies, we can write a second equation based on the total amount of money Jessica has:
10d + 25q = 10(2d) + 25(q) (Equation 2)
Now we can solve the system of equations:
- Substitute d = 16 - q into Equation 2.
- Simplify to find the value of q (the number of quarters).
- Substitute the value of q back into d = 16 - q to find the number of dimes.
Through this process, we discover that Jessica has 14 dimes and 2 quarters, which means that Whitney has 28 dimes and 2 quarters, both adding up to the same total monetary value.