Math Problem Statement

Susan has a collection of 60 nickels and dimes. If the number of nickels is three times the number of dimes, how many nickels and how many dimes does she have?

Solution

The problem you've uploaded involves finding the number of nickels and dimes in Susan's collection. Here's how we can solve it:

Let:

  • nn represent the number of nickels
  • dd represent the number of dimes

From the problem, we know two things:

  1. The total number of nickels and dimes is 60, so: n+d=60n + d = 60
  2. The number of nickels is three times the number of dimes, so: n=3dn = 3d

Now, substitute the expression for nn (from the second equation) into the first equation: 3d+d=603d + d = 60 Simplifying: 4d=604d = 60 Solving for dd: d=15d = 15

Now that we know d=15d = 15, substitute this value back into the equation n=3dn = 3d: n=3(15)=45n = 3(15) = 45

So, Susan has 45 nickels and 15 dimes.

Would you like further clarification or details on the solution? Here are some related questions:

  1. How can you set up similar equations for problems involving different coin collections?
  2. What other types of systems of equations can be used to solve real-world problems like this?
  3. How would the problem change if the number of nickels was four times the number of dimes?
  4. How can you solve equations with two variables using substitution and elimination methods?
  5. How do you check the solution to such word problems?

Tip: When solving word problems involving a system of equations, start by translating the conditions into algebraic expressions. This makes it easier to set up and solve.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Word Problems

Formulas

n + d = 60
n = 3d

Theorems

Substitution Method for Solving Equations

Suitable Grade Level

Grades 7-9