Math Problem Statement
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:
- represent the number of nickels
- represent the number of dimes
From the problem, we know two things:
- The total number of nickels and dimes is 60, so:
- The number of nickels is three times the number of dimes, so:
Now, substitute the expression for (from the second equation) into the first equation: Simplifying: Solving for :
Now that we know , substitute this value back into the equation :
So, Susan has 45 nickels and 15 dimes.
Would you like further clarification or details on the solution? Here are some related questions:
- How can you set up similar equations for problems involving different coin collections?
- What other types of systems of equations can be used to solve real-world problems like this?
- How would the problem change if the number of nickels was four times the number of dimes?
- How can you solve equations with two variables using substitution and elimination methods?
- 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
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