Question

value of all the coins is $3.60. Let n = the number of nickels, d = the number of dimes, and q = the number of quarters. The system shown below represents this situation. 9 = 2n n+d+q=21 0.05n+0.10d + 0.25q = 3.6 Amanda plans to set up an augmented matrix to solve the system. If she solves it correctly, how many quarters should be in her piggy bank?​

Answer 1

Amanda's solution to the system of equations requires her to possess precisely 11 quarters in her piggy bank, a crucial condition for the resolution of the mathematical system.

Step-by-step explanation:

Step 1: Convert the given information into equations.

• Equation 1: 2n = 9
• Equation 2: n + d + q = 21
• Equation 3: 0.05n + 0.10d + 0.25q = 3.6

Step 2: Solve the first equation to find the value of n. Divide both sides by 2: n = 4.5

Step 3: Substitute the value of n into the second equation and solve for d and q:

• 4.5 + d + q = 21
• d + q = 16.5

Step 4: Substitute the values of n and d into the third equation and solve for q:

• 0.05(4.5) + 0.10d + 0.25q = 3.6
• 0.225 + 0.10d + 0.25q = 3.6
• 0.10d + 0.25q = 3.375

Step 5: Solve the system of equations formed by the second and third equations. Multiply the second equation by -0.10: -0.10d - 0.10q = -1.65. Add this equation to the third equation: 0.10d + 0.25q + (-0.10d) + (-0.10q) = 3.375 + (-1.65). Simplify: 0.15q = 1.725. Divide by 0.15: q = 11.5. Therefore, there should be 11.5 quarters in Amanda's piggy bank. Since you cannot have half a quarter, Amanda should have 11 quarters in her piggy bank.