Question
Two 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
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
Answers
GPT-4o mini
To determine after how many weeks siblings A and 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 \( x \).
Sibling A's savings equation is:
\[ y = 10x + 25 \]
Sibling B's savings equation is:
\[ y = 5x + 50 \]
Setting the equations equal to each other:
\[ 10x + 25 = 5x + 50 \]
Next, we will isolate \( x \):
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 by 5:
\[ x = 5 \]
Thus, after **5 weeks**, both siblings will have the same amount of money in their savings accounts.
Therefore, the answer is:
**5 weeks**.
Sibling A's savings equation is:
\[ y = 10x + 25 \]
Sibling B's savings equation is:
\[ y = 5x + 50 \]
Setting the equations equal to each other:
\[ 10x + 25 = 5x + 50 \]
Next, we will isolate \( x \):
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 by 5:
\[ x = 5 \]
Thus, after **5 weeks**, both siblings will have the same amount of money in their savings accounts.
Therefore, the answer is:
**5 weeks**.