Cody has 22 rate coins. Each year Clark plans to add 15 coins to his collection. How many years will it take Cody to collect 577 coins.

Question

Determine the correct equation and solution for this situation.

Answer 1

To determine how many years it will take Cody to collect 577 coins, we can set up an equation based on the information provided.

1. Initial coins Cody has: 22 coins
2. Coins added per year: 15 coins
3. Target number of coins: 577 coins

Let \( y \) represent the number of years it will take for Cody to reach 577 coins.

After \( y \) years, the total number of coins Cody will have can be expressed as:

\[ \text{Total coins} = \text{Initial coins} + (\text{Coins added per year} \times \text{Number of years}) \]

Substituting the known values into the equation, we get:

\[ 577 = 22 + 15y \]

Next, we can solve this equation for \( y \):

1. Subtract 22 from both sides:

\[ 577 - 22 = 15y \] \[ 555 = 15y \]

2. Now, divide both sides by 15:

\[ y = \frac{555}{15} \]

3. Calculating that gives:

\[ y = 37 \]

So, it will take Cody 37 years to collect 577 coins.

The correct equation we derived was \( 577 = 22 + 15y \), and the solution was \( y = 37 \).