4) Luca has \( 19 \nmid \) in nickels and pennies. He has 7 coins altogether. How many coins of each kind does he have? nickels pennies Submit

To determine how many nickels and pennies Luca has, let's set up a system of equations based on the information provided. **Let:** - \( n \) = number of nickels - \( p \) = number of pennies **Given:** 1. The total number of coins is 7. \[ n + p = 7 \] 2. The total value of the coins is 19 cents. \[ 5n + p = 19 \] **Step 1:** Subtract the first equation from the second to eliminate \( p \): \[ (5n + p) - (n + p) = 19 - 7 \] \[ 4n = 12 \] \[ n = 3 \] **Step 2:** Substitute \( n = 3 \) back into the first equation to find \( p \): \[ 3 + p = 7 \] \[ p = 4 \] **Conclusion:** - **Nickels:** 3 - **Pennies:** 4 **Verification:** \[ 3 \text{ nickels} \times 5\text{ cents} = 15\text{ cents} \] \[ 4 \text{ pennies} \times 1\text{ cent} = 4\text{ cents} \] \[ 15\text{ cents} + 4\text{ cents} = 19\text{ cents} \] The calculations are correct. **Final Answer:** - **Nickels:** 3 - **Pennies:** 4