NAdia has 7 more nickels than dean has dimes. If dean gives nadia 4 of his dimes, then dean will have the same value of money as nadia. how much money do they have together (nadia only has nickels and dean only has dimes)

ned has nickels, has dimes, and quincy has quarters. has five more dimes than quincy has quarters. if ned gives a nickel, gives quincy a dimes, and quincy gives ned a quarter, they will alll have the same value of money. How many coins did they have originally

Try to turn each of these problems into algebraic statements with the numbers of each type of coin as an unknown. There will be as many equations as types of coins. Solve the simultaneous equations for the answers.

We will be glad to critique your work.

To solve this problem, we can work through each scenario step by step.

1. Nadia has 7 more nickels than Dean has dimes.
- Let's assume Dean has "x" dimes.
- So, Nadia has "x + 7" nickels.

2. If Dean gives Nadia 4 of his dimes, then Dean will have the same amount of money as Nadia.
- Dean's new total is "x - 4" dimes.
- To have the same value as Dean's dimes, Nadia must have the same value in nickels.

Now, let's calculate the value of dimes and nickels.

3. The value of Dean's original dimes:
- Each dime is worth $0.10.
- So, the value of Dean's original dimes is 0.10 * x.

4. The value of Nadia's original nickels:
- Each nickel is worth $0.05.
- So, the value of Nadia's original nickels is 0.05 * (x + 7).

5. Since Dean gives 4 dimes to Nadia, the value of Dean's new dimes is:
- Each dime is worth $0.10.
- So, the value of Dean's new dimes is 0.10 * (x - 4).

6. We know that the value of Dean's new dimes is equal to the value of Nadia's original nickels.
- Setting the two equations equal to each other:
0.10 * (x - 4) = 0.05 * (x + 7)

- Let's solve for x:

0.10x - 0.40 = 0.05x + 0.35
0.10x - 0.05x = 0.35 + 0.40
0.05x = 0.75
x = 0.75 / 0.05 = 15

7. We have found that Dean has 15 dimes. Using this information, we can find Nadia's number of nickels:
- Nadia has 7 more nickels than Dean, so she has 15 + 7 = 22 nickels.

Now, we can calculate the total amount of money they have together.

8. The total value of Dean's dimes:
- Each dime is worth $0.10.
- So, the total value of Dean's dimes is 0.10 * 15 = $1.50.

9. The total value of Nadia's nickels:
- Each nickel is worth $0.05.
- So, the total value of Nadia's nickels is 0.05 * 22 = $1.10.

10. The total amount of money they have together is the sum of their individual amounts:
- $1.50 + $1.10 = $2.60.

Therefore, Nadia and Dean have a total of $2.60 together.

Regarding the second scenario, it seems to contain some inconsistencies. Can you please clarify the information about Ned, , and Quincy? Specifically, how many coins does Ned have, how many coins does have, and how many coins does Quincy have originally?