Joseph and Mark have $230. Joseph and Kelvin have $130. Mark has 3 times as much money as Keivin. How much money does Kelvin have?
Let K be the amount of money Kelvin has.
Mark: 3K
Joseph: 230 - 3K
Joseph + Kelvin = 130
230 - 3K + K = 130
-2K = -100
K = <<50=50>>50. Answer: \boxed{50}.
Let's solve the problem step by step.
Let's assume the amount of money Kevin has as x dollars.
From the given information, we know that Joseph and Mark have a total of $230. So we can write the equation as:
Joseph's money + Mark's money = $230
Since we don't know Joseph's or Mark's individual amounts, we'll use variables for them. Let's say Joseph has y dollars and Mark has z dollars. Then the equation can be written as:
y + z = $230 ...(Equation 1)
Next, we know that Joseph and Kelvin have a total of $130. So we can write the equation as:
Joseph's money + Kelvin's money = $130
Again, we'll use variables for Joseph's and Kelvin's amounts. Let's say Joseph has y dollars and Kelvin has x dollars. Then the equation can be written as:
y + x = $130 ...(Equation 2)
Finally, we know that Mark has three times as much money as Kevin. So we can write the equation as:
z = 3x ...(Equation 3)
Now, let's solve these equations together.
We can rewrite Equation 1 as y = $230 - z.
We can rewrite Equation 2 as y = $130 - x.
Now, setting the two expressions for y equal, we get:
$230 - z = $130 - x
Rearranging the equation, we can express z in terms of x:
z = $230 - $130 + x
z = $100 + x ...(Equation 4)
Substituting Equation 4 into Equation 3, we get:
$100 + x = 3x
Subtracting x from both sides, we get:
$100 = 2x
Dividing both sides by 2, we get:
$50 = x
Therefore, Kelvin has $50.