SOLUTION: I have a triangle PQR. Point G is located between P&Q and point J is located between P&R. Given the information below I need to find the values of x and y so that JG is parallel to

Question 277136: I have a triangle PQR. Point G is located between P&Q and point J is located between P&R. Given the information below I need to find the values of x and y so that JG is parallel to RQ.
RQ=10
JG=8
PJ=8x-5
JR=x
PG=3y+2
QG=y
(I know that the answer's are 5/4 and 2 but I am not sure how??????)
Thanks for your help.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
for JG to be parallel to RQ, the two sides (PQ and PR) must be divided in equal ratios by JG
___ this is the same ratio as JG/RQ

PJ / (PJ + JR) = JG / RQ

(8x - 5) / (8X - 5 + x) = 8 / 10 ___ 80x - 50 = 72x - 40 ___ 8x = 10 ___ x = 5/4

PG / (PG + QG) = JG / RQ

(3y + 2) / (3y + 2 + y) = 8 / 10 ___ 30y + 20 = 32y + 16 ___ 4 = 2y ___ 2 = y
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