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 = 7x + 40, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 60.
Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?
100 weeks
12 weeks
10 weeks
5 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?
100 weeks
12 weeks
10 weeks
5 weeks
Answers
GPT-4o mini
To find out when the savings of sibling A and sibling B are equal, we need to set the two equations equal to each other and solve for \( x \).
The equations are:
1. \( y = 7x + 40 \) (sibling A's savings)
2. \( y = 5x + 60 \) (sibling B's savings)
Set the equations equal:
\[ 7x + 40 = 5x + 60 \]
Now, simplify and solve for \( x \):
1. Subtract \( 5x \) from both sides:
\[ 7x - 5x + 40 = 60 \]
\[ 2x + 40 = 60 \]
2. Subtract 40 from both sides:
\[ 2x = 60 - 40 \]
\[ 2x = 20 \]
3. Divide both sides by 2:
\[ x = 10 \]
So, after 10 weeks, sibling A and sibling B will have the same amount of money in their savings accounts.
The answer is **10 weeks**.
The equations are:
1. \( y = 7x + 40 \) (sibling A's savings)
2. \( y = 5x + 60 \) (sibling B's savings)
Set the equations equal:
\[ 7x + 40 = 5x + 60 \]
Now, simplify and solve for \( x \):
1. Subtract \( 5x \) from both sides:
\[ 7x - 5x + 40 = 60 \]
\[ 2x + 40 = 60 \]
2. Subtract 40 from both sides:
\[ 2x = 60 - 40 \]
\[ 2x = 20 \]
3. Divide both sides by 2:
\[ x = 10 \]
So, after 10 weeks, sibling A and sibling B will have the same amount of money in their savings accounts.
The answer is **10 weeks**.