Final answer:
Steve has 211 quarters and 216 dimes in his piggy bank, calculated by setting up equations based on the values of quarters and dimes and the total amount of money.
Step-by-step explanation:
The student asked how many quarters and dimes are in Steve's piggy bank if he has five more dimes than quarters and the total amount of money is $74.35. To solve this problem, we can set up two equations based on the given information. Let q represent the number of quarters and d represent the number of dimes. Therefore, d = q + 5 because Steve has five more dimes than quarters.
Since each quarter is worth $0.25 and each dime is worth $0.10, we can set up an equation to express the total amount of money in the piggy bank: 0.25q + 0.10d = 74.35. Substituting the expression for d from the first equation, we have 0.25q + 0.10(q + 5) = 74.35.
Now, we solve for q:
- Multiply out the term: 0.25q + 0.10q + 0.50 = 74.35.
- Combine like terms: 0.35q + 0.50 = 74.35.
- Subtract 0.50 from both sides: 0.35q = 73.85.
- Divide both sides by 0.35 to find q: q = 211.
- Substitute q back into the expression for d to find the number of dimes: d = 211 + 5 = 216.
Steve has 211 quarters and 216 dimes in his piggy bank.