Question

1. gavin has nickels, dimes, and quarters in the ratio of 8 : 1 : 2. if 16 of gavins coins are quarters, how many nickels and dimes does gavin have?

Explanation:

Step1: Determine the multiplier for the ratio

The ratio of nickels : dimes : quarters is \(8:1:2\). Let the common multiplier be \(x\). So the number of quarters is \(2x\). We know the number of quarters is 16, so we set up the equation \(2x = 16\). Solving for \(x\), we divide both sides by 2: \(x=\frac{16}{2}=8\).

Step2: Calculate the number of nickels and dimes

• Number of nickels: The ratio for nickels is 8, so the number of nickels is \(8x\). Substituting \(x = 8\), we get \(8\times8 = 64\).
• Number of dimes: The ratio for dimes is 1, so the number of dimes is \(1\times x=8\).

Step3: Find the total number of nickels and dimes

To find the total number of nickels and dimes, we add the number of nickels and dimes: \(64 + 8=72\).

Answer:

72