Brandon is running errands for his mother.
It is

1/4
mile from his house to the library and
2/3
mile from the library to the grocery store.
Brandon claims that he walks a total of
11/12
mile if he goes from his house to the library to the grocery store.
Which of the following shows whether Brandon is correct and why?

you can't solve x because it is 2 linear equation and you only have one equation

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