SOLUTION: If P bisects KM, PK=5v+7, and PM=10v-13,Find v and KM

Question 1057895: If P bisects KM, PK=5v+7, and PM=10v-13,Find v and KM
Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
Since P bisects KM, P is the midpoint between K and M, and thus PK = PM.

This gives:

5v + 7 = 10v - 13

Subtracting 5v from both sides gives:

7 = 5v - 13

5v - 13 = 7

Adding 13 to both sides gives:

5v = 7 + 13

5v = 20

Dividing both sides by 5 then gives:

v = 4

Using v = 4, PK = 5(4) + 7 = 27.

Thus, KM = 2*PK = 2*27 = 54

As a check, calculate PM to see that PM = PK:

PM = 10(4) - 13 = 40 - 13 = 27 = PK.
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