https://file.aiquickdraw.com/mathbot/file/1726370007556rqucft6m.jpg

It looks like the problem involves a box containing 50 coins made up of pennies, dimes, and quarters, and their total value is $5.87. We also know that the number of pennies equals the number of dimes.

Let's break down the problem:

### Variables:
1. Let $ x $ represent the number of pennies.
2. Since the number of pennies equals the number of dimes, we can also say that the number of dimes is $ x $.
3. Let $ y $ represent the number of quarters.

### Total number of coins:
The total number of coins is 50:
\[
x + x + y = 50
\]
This simplifies to:
\[
2x + y = 50 \quad \text{(Equation 1)}
\]

### Total value:
The total value of the coins is $5.87, or 587 cents. The value contributions are:
- Pennies: $ 0.01x $
- Dimes: $ 0.10x $
- Quarters: $ 0.25y $

The total value in cents is:
\[
0.01x + 0.10x + 0.25y = 5.87
\]
Multiply the equation by 100 to get rid of the decimals:
\[
x + 10x + 25y = 587
\]
This simplifies to:
\[
11x + 25y = 587 \quad \text{(Equation 2)}
\]

### Solving the system of equations:
We now have two equations:
1. $ 2x + y = 50 $
2. $ 11x + 25y = 587 $

I'll solve this system of equations to find $ x $ and $ y $.The solution to the system of equations is:
- $ x = 17 $ (so there are 17 pennies and 17 dimes),
- $ y = 16 $ (there are 16 quarters).

### Breakdown:
- 17 pennies,
- 17 dimes,
- 16 quarters.

These add up to a total of 50 coins and a value of $5.87.

Would you like further clarification or more details on this? Here are five related questions you might want to explore:

1. How would the solution change if the total value of the coins were different?
2. How can we verify the total value using the number of pennies, dimes, and quarters?
3. What if the number of dimes was twice the number of pennies?
4. How would we solve the system if we only had the number of pennies and the total value?
5. Can this method work for different combinations of coins (e.g., nickels instead of dimes)?

**Tip:** When solving word problems, always define your variables clearly and set up equations based on the conditions provided.

A box currently contains 50 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $5.87. How many of each denomination does the box have?

Learn how to solve a word problem involving 50 coins made up of pennies, dimes, and quarters. The total value is $5.87, and the number of pennies equals the number of dimes. This algebraic problem is solved using a system of linear equations, suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation