Cody has 22 rare 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.

(1 point)
Responses

15 + 22y = 577; 37 years
15 + 22y = 577; 37 years

15y + 22 = 577; 37 years
15y + 22 = 577; 37 years

37y = 577; 16 years
37y = 577; 16 years

7y = 577; 82 years
7y = 577; 82 years

Answer 1

To determine how long it will take for Cody to collect 577 coins, we can set up an equation based on the information provided. Cody starts with 22 coins and adds 15 coins each year. Let \( y \) represent the number of years. The total number of coins Cody will have after \( y \) years can be described by the equation:

\[ \text{Total coins} = \text{Initial coins} + \text{Coins added each year} \times \text{Number of years} \] \[ 577 = 22 + 15y \]

We now need to solve for \( y \):

1. Subtract 22 from both sides: \[ 577 - 22 = 15y \] \[ 555 = 15y \]

2. Divide both sides by 15: \[ y = \frac{555}{15} \] \[ y = 37 \]

Thus, it will take Cody 37 years to collect 577 coins. The correct equation is:

\[ 15y + 22 = 577; \text{ 37 years} \]

So the answer is:

15y + 22 = 577; 37 years