A person has four times as many nickels as quarters. If the total face value of these coins is $2.25, how many of each type of coin does this person have?



nickels
 
quarters
 

Let the number of quarters be denoted by $ q $, and the number of nickels be $ n $. From the problem, we know two things:

1. The number of nickels is four times the number of quarters:  
   \[
   n = 4q
   \]
   
2. The total value of the coins is $2.25, which is 225 cents.

   - Each quarter is worth 25 cents, so the value of $ q $ quarters is $ 25q $ cents.
   - Each nickel is worth 5 cents, so the value of $ n $ nickels is $ 5n $ cents.

The total value of the nickels and quarters together is 225 cents, so we can write the equation:
\[
5n + 25q = 225
\]

Now, substitute $ n = 4q $ into the equation:
\[
5(4q) + 25q = 225
\]
Simplify:
\[
20q + 25q = 225
\]
\[
45q = 225
\]
Solve for $ q $:
\[
q = \frac{225}{45} = 5
\]

Now that we know $ q = 5 $, we can find $ n $:
\[
n = 4q = 4(5) = 20
\]

Thus, the person has:
- 5 quarters
- 20 nickels

Would you like more details or have any questions?

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Here are 5 related questions for further practice:
1. If the person had twice as many quarters, what would be the total value?
2. What if the total value was $3.50? How many nickels and quarters would the person have?
3. If the person had 10 dimes instead of nickels, what would be the total value?
4. How many pennies would make the same total value as the coins in this problem?
5. What if the person had an equal number of nickels and quarters? What would the total value be?

**Tip**: Always check the relationships between variables (like the ratio between nickels and quarters here) before solving the equations.

A person has four times as many nickels as quarters. If the total face value of these coins is $2.25, how many of each type of coin does this person have?

Learn how to solve a coin value problem where a person has four times as many nickels as quarters, with a total value of $2.25. This step-by-step solution uses algebraic equations to determine the number of each coin. Suitable for students in Grades 6-8.

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