My child came home with an assignment on line segments. one of the problems is rs=2x st=3x rt=25 Their teacher told them that the solution is 15. My question is how did they come to this answer ?
r, s, and t are points along a line. r and t are the end points. rs, st and rt are the disatnces between the points.
rs + st = rt = 25 = 3x + 2x = 5x
Therefore x = 5
In this case st = 15 and rs = 10. It is not clear what the question was asking for. Was it the length of st?
To find the value of x in this problem, we can use the fact that the sum of the lengths of two line segments is equal to the length of their combined line segment.
In this case, we have three line segments: rs, st, and rt.
Given that rs = 2x, st = 3x, and rt = 25, we can set up an equation to represent the relationship between these line segments:
rs + st = rt
Substituting the given values, we get:
2x + 3x = 25
Combining like terms, we have:
5x = 25
To find the value of x, we can divide both sides of the equation by 5:
5x / 5 = 25 / 5
Simplifying, we get:
x = 5
So, the value of x is 5.
To find the length of the line segment rt, we can substitute the value of x back into the equation for rt:
rt = 25
rt = 3x
Substituting x = 5, we have:
rt = 3(5)
rt = 15
Therefore, the length of the line segment rt is 15 units. This is how the teacher arrived at the answer of 15.