Final answer:
After setting up a system of equations to represent the value of dimes and quarters Tyler has, and solving for the number of dimes, it is determined that Tyler has 7 dimes.
Step-by-step explanation:
Tyler has $9.70 in dimes and quarters. The question states that the number of quarters is eight more than four times the number of dimes. We can set up a system of equations to solve for the number of dimes Tyler has. Let d represent the number of dimes and q represent the number of quarters. Each dime is worth 10 cents and each quarter is worth 25 cents.
The total value equation is 10d + 25q = 970 (since we have $9.70, and we need to work in pennies to match the values of dimes and quarters).
The relationship between dimes and quarters can be written as q = 4d + 8.
Substituting the second equation into the first gives us 10d + 25(4d + 8) = 970. Simplifying this, we get 10d + 100d + 200 = 970, which simplifies further to 110d = 770. Dividing both sides by 110 gives us d = 7.
Therefore, the correct answer is d. 7 dimes.