Math Problem Statement

John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to

determine the number of dimes, x, in his pocket?

Solution

Let's define the variables and translate the situation into a mathematical equation:

  1. Number of dimes (x): Let xx represent the number of dimes John has in his pocket.
  2. Number of nickels: Since John has four more nickels than dimes, the number of nickels is x+4x + 4.

Coin Values:

  • A dime is worth 0.100.10 dollars.
  • A nickel is worth 0.050.05 dollars.

Total Value:

The total value of the coins in John's pocket is 1.251.25 dollars. The equation for this relationship is: 0.10x+0.05(x+4)=1.250.10x + 0.05(x + 4) = 1.25

Simplifying the Equation:

Expand and simplify: 0.10x+0.05x+0.20=1.250.10x + 0.05x + 0.20 = 1.25 0.15x+0.20=1.250.15x + 0.20 = 1.25 0.15x=1.050.15x = 1.05

The simplified equation is: x=1.050.15x = \frac{1.05}{0.15}

This equation can be solved to find xx, the number of dimes.


Would you like me to solve this equation or provide further clarification? 😊

Related Questions:

  1. What is the exact number of dimes John has?
  2. How many nickels are in John's pocket?
  3. How does the value of each type of coin contribute to the total?
  4. Can this problem be solved using integers instead of decimals? Why or why not?
  5. What would the equation look like if John had four fewer nickels than dimes?

Tip:

When solving money-related problems, converting values into cents (e.g., 10¢ and 5¢) can help avoid decimal arithmetic errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Currency Arithmetic

Formulas

0.10x + 0.05(x + 4) = 1.25

Theorems

Basic properties of equality

Suitable Grade Level

Grades 6-8