Question

wo siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

2.5 weeks
5 weeks
15 weeks
75 weeks

Answer 1

To find out after how many weeks sibling A and sibling B will have the same amount of money in their savings accounts, we need to set the two equations equal to each other and solve for \( x \).

The equations are:

1. For sibling A: \( y = 10x + 25 \)
2. For sibling B: \( y = 5x + 50 \)

Setting them equal:

\[
10x + 25 = 5x + 50
\]

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

1. Subtract \( 5x \) from both sides:

\[
10x - 5x + 25 = 50
\]
\[
5x + 25 = 50
\]

2. Subtract 25 from both sides:

\[
5x = 50 - 25
\]
\[
5x = 25
\]

3. Divide both sides by 5:

\[
x = \frac{25}{5} = 5
\]

Therefore, after **5 weeks**, their savings accounts will have the same amount of money.

The correct answer is **5 weeks**.