= Andy took a total of 27 quizzes over the course of 3 weeks. How many weeks of school will Andy have to attend this quarter before he will have taken a total of 45 quizzes?

2 weeks

Step-by-step explanation:

27/3 = 9, this means that he is doing 9 quizzes per week.

45- 27 = 18 quizzes left

if he is completing 9 quizzes per week 18/9 = 2, so it will take him 2 weeks  

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