If AB=3x, BC=2y+16, AC=60 and B is midpoint of AC, what are the values of x and y?
To find the values of x and y, we can set up equations based on the given information.
First, let's use the fact that B is the midpoint of AC. This means that AB is equal to BC. Therefore, we can write the equation:
AB = BC
Substituting the given values, we have:
3x = 2y + 16
Now, let's use the length of AC. We know that AC is equal to 60. Since B is the midpoint, we can express AC as the sum of AB and BC:
AC = AB + BC
Substituting the given values, we have:
60 = 3x + (2y + 16)
Simplifying the equation, we have:
60 = 3x + 2y + 16
Combining like terms, we get:
3x + 2y = 60 - 16
3x + 2y = 44
We now have a system of two equations:
3x = 2y + 16
3x + 2y = 44
To solve this system, we can use the method of substitution or elimination.
Let's use the method of substitution. From the first equation, we can solve for x in terms of y:
3x = 2y + 16
x = (2y + 16)/3
Now, substitute this expression for x in the second equation:
3[(2y + 16)/3] + 2y = 44
Simplifying, we have:
2y + 16 + 2y = 44
Combining like terms, we get:
4y + 16 = 44
Subtracting 16 from both sides, we have:
4y = 44 - 16
4y = 28
Dividing both sides by 4, we get:
y = 7
Now, substitute this value of y back into the first equation to find the value of x:
3x = 2(7) + 16
3x = 14 + 16
3x = 30
Dividing both sides by 3, we get:
x = 10
Therefore, the values of x and y are 10 and 7, respectively.