Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Zachary and Valentina are making presentations for a class project. Zachary's slideshow starts with a verbal introduction that is 15 seconds long, and then each slide is left up for 11 seconds. Valentina leaves each slide onscreen for 8 seconds, and her introduction lasts 18 seconds. Zachary and Valentina notice that their presentations have both the same number of slides and the same duration. How many slides are in each presentation? How long is each presentation?

step-by-step explanation:

there are no multiple choices

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft