the larger of 2 numbers is twice the smaller number if 12 is subtracted from the larger number the result is 7 more than the smaller number

Step-by-step explanation:

Let x be the smaller number

Let y be the larger number

The larger of 2 numbers is twice the smaller number :

if 12 is subtracted from the larger number the result is 7 more than the smaller number :

To solve for x  ;

Substitute 2x for y in the second equation

To solve for y

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