Final answer:
To solve the problem, we use a system of equations with variables representing the number of pennies and quarters. Two equations are set up: one for the total number of coins and another for their total value. By solving the system, we find the correct combination of pennies and quarters to meet the conditions.
Step-by-step explanation:
To solve the problem of selecting 15 coins worth exactly $4.35 from a jar of pennies and quarters, we need to formulate a system of equations. Let's denote the number of pennies as 'p' and the number of quarters as 'q'.
Our first equation represents the total number of coins:
p + q = 15 (Equation 1)
The second equation represents the total value of all coins, noting that a penny is worth $0.01 and a quarter is worth $0.25:
0.01p + 0.25q = 4.35 (Equation 2)
To solve the system, we can use the substitution or elimination method. With the substitution method, we can solve Equation 1 for 'p':
p = 15 - q
Then substitute 'p' into Equation 2 and solve for 'q'. With the elimination method, we can multiply Equation 1 by -0.01 to make the coefficients of 'p' in both equations match and then add them together to eliminate 'p' and solve for 'q'.
By solving the equations, we find that we need 9 pennies and 6 quarters to have a total of 15 coins worth $4.35.