We can represent the given information in a line segment for reference as shown in the following image:
Since AB=3x
And BC=10
And AC=4x+1
As we can see the sum of AB and BC (3x and 10) gives AC as the result.
So we will have an equation in which the addition of 3x+10 is equal to 4x+1:
Now we need to solve this equation for x.
Subtract 3x to both sides:
Combine like terms on the right side:
And subtract 1 to both sides:
The value of x is 9.
Using that value, we find AB:
And we do the same to find AC:
Answer:
x=9
AB=27
AC=37