Final answer:
Betty has a total of 24 coins consisting of 7 quarters and 17 dimes, which together make $3.45.
Step-by-step explanation:
To determine how many coins Betty has if Betty had 10 more dimes than quarters, and if she had a total of $3.45, we first need to set up equations based on the information provided. Let's denote the number of quarters as q and the number of dimes as d. Since each quarter is worth $0.25 and each dime is worth $0.10, we can create the following equations:
- The total amount of money in quarters and dimes is $3.45: 0.25q + 0.10d = 3.45.
- Betty has 10 more dimes than quarters: d = q + 10.
Substituting the second equation into the first gives us:
0.25q + 0.10(q + 10) = 3.45
Now, simplify and solve for q:
0.25q + 0.10q + 1 = 3.45
0.35q + 1 = 3.45
0.35q = 2.45
q = 2.45 / 0.35
q = 7
Since q (the number of quarters) is 7, we use the second equation to find d (the number of dimes):
d = 7 + 10
d = 17
Therefore, Betty has 7 quarters and 17 dimes, which means she has a total of 24 coins.