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

Answer 1

Let's break down the situation and write an equation to solve for the number of years it will take Cody to collect 577 coins.

Cody starts with 22 coins and adds 15 coins each year. We want to find out how many years (let's call this \( y \)) it will take for Cody to reach a total of 577 coins.

The total number of coins Cody will have after \( y \) years can be expressed as:

\[ \text{Total Coins} = \text{Initial Coins} + \text{Coins Added Each Year} \times \text{Number of Years} \] \[ \text{Total Coins} = 22 + 15y \]

We want this total to equal 577:

\[ 22 + 15y = 577 \]

Now, we can solve for \( y \):

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

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

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

Thus, the correct equation is \( 15y + 22 = 577 \) and the number of years is 37.

The final statement is: 15y + 22 = 577; 37 years.