Question

Sonia opened a savings account and then added the same amount to the savings account every week. After 5
weeks, her savings account had a total of $45
. After 10
weeks, her savings account had a total of $70
. Which equation represents the amount of money (y)
in dollars, in Sonia’s savings account after x
weeks?
A
y=7xy=7xy=7x
B
y=5x+20y=5x+20y=5x+20
C
y=2x+5y=2x+5y=2x+5
D
y=9xy=9xy=9x

Answer 1

To determine the correct equation representing the amount of money \( y \) in Sonia's savings account after \( x \) weeks, we can analyze the information provided.

After 5 weeks, the total in the account is $45:
\[
y = 45 \quad \text{when} \quad x = 5
\]

After 10 weeks, the total in the account is $70:
\[
y = 70 \quad \text{when} \quad x = 10
\]

Let's denote the amount added each week as \( a \). Therefore, the total amount in the savings account can be represented by the equation:
\[
y = a \cdot x + C
\]
where \( C \) is the initial amount in the account.

### Step 1: Set up equations

Using the information from the 5th and 10th weeks, we can create the following equations:

1. For \( x = 5 \):
\[
y = a \cdot 5 + C = 45 \quad \text{(1)}
\]

2. For \( x = 10 \):
\[
y = a \cdot 10 + C = 70 \quad \text{(2)}
\]

### Step 2: Subtract equations to eliminate \( C \)

Subtract equation (1) from equation (2):
\[
(a \cdot 10 + C) - (a \cdot 5 + C) = 70 - 45
\]

This simplifies to:
\[
5a = 25
\]

Solving for \( a \):
\[
a = 5
\]

### Step 3: Substitute \( a \) back to find \( C \)

Now that we have \( a \), we can substitute it back into equation (1) to find \( C \):
\[
5 \cdot 5 + C = 45
\]
\[
25 + C = 45
\]
\[
C = 20
\]

### Step 4: Write the equation for \( y \)

We have found \( a = 5 \) and \( C = 20 \). Now we can write the equation for \( y \):
\[
y = 5x + 20
\]

### Select the correct option:

Based on the options provided, the correct equation is:
**B** \( y = 5x + 20 \)