A ball and a bat cost $110 total. The bat costs $100 more than the ball. How much does the ball cost?
For this system of equation,
I designated x for the ball and y for the bat. I know that both equal to 110.
So I wrote the first equation as
x+y=110
I don't know how to proceed for the second equation.
Since the ball is less than the bat, would it be subtracted?
Do it with one variable:
cost of ball ---- x
cost of bat = x + 100
x + x + 100 = 110
2x = 10
x = 5
ball costs $5, bat costs $105
your way:
x+y = 110
y - x = 100
Add them: 2y = 210
y = 105
sub back into the first and do it mentally, x = 5
To determine the second equation, you need to use the information given about the cost of the bat being $100 more than the ball.
Let's assign x for the cost of the ball. Since the cost of the bat is $100 more than the ball, the cost of the bat can be represented as (x + $100).
So, the second equation can be written as:
x + (x + $100) = $110
Now, you can simplify the equation by combining like terms:
2x + $100 = $110
To isolate 2x, you can subtract $100 from both sides of the equation:
2x = $110 - $100
2x = $10
Finally, divide both sides of the equation by 2 to solve for x:
x = $10 / 2
x = $5
Therefore, the ball costs $5.