Final answer:
To determine the number of dimes and pennies Taylor has, we used an equation 10d + (d + 2) = 200, where d represents the number of dimes. Solving the equation, we found that Taylor has 18 dimes and 20 pennies.
Step-by-step explanation:
The question asks us to write an equation that represents the situation where Taylor has $2.00 in dimes and pennies, and the number of pennies is 2 more than the number of dimes. We need to solve this equation to find the number of each coin.
Since we know that there are 100 pennies in a dollar, we can say that Taylor has 200 pennies' worth of money. Let's let the number of dimes be represented by d, and since each dime is worth 10 pennies, the value of the dimes in pennies is 10d. The number of pennies is 2 more than the number of dimes, so the number of pennies is d + 2.
Combining the values of the dimes and the pennies, the following equation represents the total amount of money Taylor has:
10d + (d + 2) = 200
Now, we solve for d:
- Combine like terms: 11d + 2 = 200
- Subtract 2 from both sides: 11d = 198
- Divide both sides by 11: d = 18
So, Taylor has 18 dimes. Since we know the number of pennies is 2 more than the number of dimes, Taylor has 18 + 2 pennies, which means she has 20 pennies.