Question

8. The sum of the numbers p, q, and r is 80. the ratio of p to r is 3 to 5. The ratio of r to q is 10 to 4. What is the value of pq?A. 308B. 362C. 384D. 412

Answer 1

Well, let's gather the information. And set the equations.

p+q+r=80

p/r =3/5 this is the same as 3r=5p p=3/5r or r= 5/3p

r/q=10/4 this is the same as 10q=4r so or r=5/2q q=4/10r simplifying q =2/5r

Let's plugg it in the first equation:

p+q+r=80

p+q+5/2q=80

p+2/5r+5/2q=80

p+2/5r+5/2q=80

p+2/5(5/3)p+5/2q=80

p+2/3p+5/2q=80

p+2/3p=80-5/2q

5/3p=80-5/2q x 3

5p=240-15/2q :5

p=48-3/2q

(48-3/2q)+q+5/2q=80

48-3/2q+q+5/2q=80

48-2/2q+q=80

48+2q=80

2q=80-48

2q=32

q=16

p=48-3/2(16)

p=48-3/2

p=24

pq=24*32=384

The answer is C) 384