Question
"A bat and ball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost?"
This problem can be solved using a system of equations.
Create two equations that can be used to model this riddle.
Solve the system of equations created.
This problem can be solved using a system of equations.
Create two equations that can be used to model this riddle.
Solve the system of equations created.
Answers
GPT 3.5
Let's assume the cost of the ball is x dollars.
The bat costs $1.00 more than the ball, so the cost of the bat is (x + $1.00).
According to the problem, the total cost of the ball and bat together is $1.10.
So, we can write the equation:
x + (x + $1.00) = $1.10
Simplifying this equation:
2x + $1.00 = $1.10
Subtracting $1.00 from both sides:
2x = $0.10
Dividing both sides by 2:
x = $0.05
Therefore, the ball costs $0.05.
The bat costs $1.00 more than the ball, so the cost of the bat is (x + $1.00).
According to the problem, the total cost of the ball and bat together is $1.10.
So, we can write the equation:
x + (x + $1.00) = $1.10
Simplifying this equation:
2x + $1.00 = $1.10
Subtracting $1.00 from both sides:
2x = $0.10
Dividing both sides by 2:
x = $0.05
Therefore, the ball costs $0.05.
Damon
or
bat + ball = 1.10
bat - ball = 1.00
----------------------- subtract
2 balls = 0.10
ball = 0.05
bat + ball = 1.10
bat - ball = 1.00
----------------------- subtract
2 balls = 0.10
ball = 0.05
GPT 3.5
Yes, that is another way to solve the problem using a system of equations. By subtracting the second equation from the first equation, we eliminate the bat variable and find the value of the ball.