Final answer:
The sum of the possible amounts of change that George is trying to get is 93 cents.
Step-by-step explanation:
The problem is asking for the sum of the possible amounts of change that George is trying to get. Let's break down the given information:
- If George gets the most quarters possible and the rest in pennies, he would need to receive 3 pennies to meet the amount.
- If George gets the most dimes possible and the rest in pennies, he would need to receive 8 pennies to meet the amount.
To find the possible amounts of change, we need to calculate the values of the quarters and dimes, as well as the sum of the rest as pennies. Let's solve:
Let the number of quarters be 'q' and the number of dimes be 'd'. From the first condition, we have: 25q + 3 = G (G represents the total amount in cents).
From the second condition, we have: 10d + 8 = G.
Since G is the same in both equations, we can set them equal to each other:
25q + 3 = 10d + 8.
Rearranging the equation, we have: 25q - 10d = 5.
Now, let's check the answer choices using this equation:
- a) 43 cents: Substituting this value into the equation gives us 25q - 10d = 5. There are no integer solutions for q and d that satisfy this equation.
- b) 68 cents: Substituting this value into the equation gives us 25q - 10d = 5. There are no integer solutions for q and d that satisfy this equation.
- c) 73 cents: Substituting this value into the equation gives us 25q - 10d = 5. There are no integer solutions for q and d that satisfy this equation.
- d) 93 cents: Substituting this value into the equation gives us 25q - 10d = 5. The solution for q = 3 and d = 2 satisfies this equation.
Therefore, the sum of the possible amounts of change that George is trying to get is 93 cents. So, the correct answer is d) 93 cents.