Math Problem Statement
Paula’s purse contains twice as many dimes as quarters and three fewer nickels than dimes. The total of these coins is $3.15. How many dimes are there?
Solution
Let's denote the number of quarters as , the number of dimes as , and the number of nickels as .
According to the problem, we have the following relationships:
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Twice as many dimes as quarters:
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Three fewer nickels than dimes:
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Total value of the coins is $3.15:
The value equation can be expressed in cents as:
Now, let's substitute the expressions for and in terms of into the value equation.
First, substitute into :
Now substitute and into the value equation:
Simplify and solve for :
Now that we know , we can find and :
Thus, the number of dimes is 12.
Would you like more details on this solution or have any other questions?
Here are 5 related questions for further practice:
- If Paula had 4 more dimes, what would be the new total value of the coins?
- What is the total number of coins Paula has in her purse?
- If Paula added 2 quarters, how much would the total value of her coins increase?
- How many more dimes than nickels does Paula have?
- If Paula had an equal number of nickels and quarters, what would be the new total value?
Tip: Always convert the total value into cents when working with coin problems to avoid confusion with decimals.
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Math Problem Analysis
Mathematical Concepts
Equations
System of Equations
Word Problems
Formulas
Linear equations
Value equations in cents
Theorems
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Suitable Grade Level
Grades 7-9
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