Lydia was comparing the price of grapefruit juice at two stores. The equation y = 1.7x represents what Lydia would pay in dollars and cents, y, for a bottles of
grapefruit juice at store B. Lydia can buy 7 bottles of grapefruit juice at Store A for a
total cost of $12.60.
How much less is a bottle of grapefruit juice at Store B than
at Store A?

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

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1