In the​ following, write an expression in terms of the given variables that represents the indicated quantity. The amount of money in cents in a jar containing some nickels and d dimes and some quarters if there are 4 times as many nickels as dimes and twice as many quarters as nickels.The expression for the amount of money in the jar is

Let's break down the problem step by step.

### Step 1: Define the number of coins
- Let the number of **dimes** be \( d \).
- The number of **nickels** is 4 times the number of dimes, so there are \( 4d \) nickels.
- The number of **quarters** is twice the number of nickels, so there are \( 2(4d) = 8d \) quarters.

### Step 2: Calculate the value of each type of coin
- **Nickels** are worth 5 cents each, so the total value of the nickels is \( 5 \times 4d = 20d \) cents.
- **Dimes** are worth 10 cents each, so the total value of the dimes is \( 10 \times d = 10d \) cents.
- **Quarters** are worth 25 cents each, so the total value of the quarters is \( 25 \times 8d = 200d \) cents.

### Step 3: Total value of all the coins
Now, sum the value of all the coins:
\[
\text{Total value} = 20d + 10d + 200d = 230d \, \text{cents}
\]

Thus, the expression for the total amount of money in the jar in terms of \( d \) (the number of dimes) is:
\[
\boxed{230d} \, \text{cents}.
\]

Would you like further details or have any questions?

Here are some related questions to deepen understanding:
1. How would the expression change if there were 5 times as many nickels as dimes?
2. If the jar had an additional 10 pennies, how would that affect the total amount?
3. What would the total value be if there were 10 dimes?
4. How would you represent the amount of money if there were no quarters?
5. What is the total number of coins in the jar in terms of \( d \)?

**Tip**: Always carefully define variables before writing expressions for easier problem-solving.

In the following, write an expression in terms of the given variables that represents the indicated quantity. The amount of money in cents in a jar containing some nickels and d dimes and some quarters if there are 4 times as many nickels as dimes and twice as many quarters as nickels. The expression for the amount of money in the jar is:

Learn how to find the total value of coins in a jar containing nickels, dimes, and quarters, with a detailed step-by-step algebraic expression. Understand how to calculate values when there are 4 times as many nickels as dimes and twice as many quarters as nickels. Suitable for Grades 6-8.

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