https://file.aiquickdraw.com/mathbot/file/172660211649245lqfu2e.jpg

The problem states that Jada has a coin jar containing **n** nickels and **d** dimes worth a total of **$3.65**. The given equation is $0.05n + 0.1d = 3.65$, representing the monetary value of the nickels and dimes.

We need to find an equivalent equation to the given one. Here's a breakdown:

- $0.05n$ represents the value of the nickels, as each nickel is worth 5 cents (or 0.05 dollars).
- $0.1d$ represents the value of the dimes, as each dime is worth 10 cents (or 0.10 dollars).
- The total value of the coins is $3.65, which is equivalent to 365 cents.

To convert the equation to match the integer form, we can multiply the entire equation by 100 to eliminate the decimals:
\[
0.05n + 0.1d = 3.65
\]
Multiplying through by 100:
\[
(0.05 \times 100)n + (0.1 \times 100)d = 3.65 \times 100
\]
\[
5n + 10d = 365
\]

Thus, the equivalent equation is $ \boxed{5n + 10d = 365} $.

This matches the first option in the list.

Would you like any further details or have any questions? 

Here are five related questions for deeper understanding:
1. How would you solve for the number of nickels if the number of dimes is known?
2. What if the total value was $5.00 instead of $3.65—how would the equation change?
3. How can you check if a given combination of nickels and dimes satisfies the equation?
4. Can you graph this equation to find possible values of nickels and dimes?
5. How would the equation change if pennies were also included?

**Tip**: When dealing with equations that involve money, converting everything to cents often simplifies the calculations by avoiding decimals.

Jada has a coin jar containing n nickels and d dimes worth a total of $3.65. The equation 0.05n + 0.1d = 3.65 is one way to represent this situation. Which equation is equivalent to the equation 0.05n + 0.1d = 3.65?

Explore how to convert the linear equation 0.05n + 0.1d = 3.65 into an equivalent equation using integer values. This problem involves understanding the value of coins and applying basic algebra to represent the situation. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation