Jamie has been saving pennies and nickels for a month. The number of nickels Jamie has is three more than eight times the number of pennies. Jamie has a total of $3.02 in just these coins. How many pennies and how many nickels are there?



Let $ p $ represent the number of pennies Jamie has, and $ n $ represent the number of nickels.

We are given two key pieces of information:

1. The number of nickels is three more than eight times the number of pennies:
   \[
   n = 8p + 3
   \]

2. Jamie has a total of $3.02 in pennies and nickels. Since a penny is worth $0.01 and a nickel is worth $0.05, we can set up the following equation for the total value:
   \[
   0.01p + 0.05n = 3.02
   \]

### Step 1: Substitute for $ n $ in terms of $ p $
Using the first equation $ n = 8p + 3 $, substitute $ n $ in the second equation:
\[
0.01p + 0.05(8p + 3) = 3.02
\]

### Step 2: Simplify the equation
Expanding the equation:
\[
0.01p + 0.40p + 0.15 = 3.02
\]
Combine like terms:
\[
0.41p + 0.15 = 3.02
\]

### Step 3: Solve for $ p $
Subtract 0.15 from both sides:
\[
0.41p = 2.87
\]
Now, divide by 0.41:
\[
p = \frac{2.87}{0.41} = 7
\]

### Step 4: Solve for $ n $
Now that we know $ p = 7 $, substitute this back into the first equation to find $ n $:
\[
n = 8(7) + 3 = 56 + 3 = 59
\]

### Conclusion
Jamie has:
- **7 pennies**
- **59 nickels**

---

Would you like a breakdown of any specific step, or have any questions?

1. How would the solution change if Jamie had a different total amount, say $2.52?
2. How would the number of coins change if Jamie had twice as many nickels?
3. What if the ratio of nickels to pennies was 5:1 instead?
4. How could we set up a system of equations if Jamie had dimes as well?
5. How does this approach generalize if the coins have variable values?

**Tip:** When dealing with equations involving money, ensure all values are in the same units (e.g., dollars or cents) to avoid calculation errors.

Jamie has been saving pennies and nickels for a month. The number of nickels Jamie has is three more than eight times the number of pennies. Jamie has a total of $3.02 in just these coins. How many pennies and how many nickels are there?

Find out how to solve an algebraic word problem where the number of nickels is three more than eight times the number of pennies. Learn step-by-step how to set up equations and solve for both pennies and nickels given a total value of $3.02. Perfect for students in Grades 6-8.

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