Planet 1 orbits every 4 years. Planet 2 orbits every 8 years and planet 3 orbits every 14 years around a star. When will the planets next line up in the same position

Stuck In same question Jinx

Step-by-step explanation:

-2

7 - 9 = -2

reversed:

-2 + 9 = 7

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4