Let a, b and c be positive numbers satisfying ab = 11.25; ac = 20; and bc = 36. What is the value of c?

Guest Nov 3, 2019

#1

#6**0 **

Note that most 'Answerers' are less inclined to provide methods of finding an answer to 'guest' posters and may just post an answer.....

Ever thought of signing up as a registered user? ~EP

ElectricPavlov
Nov 3, 2019

#5**0 **

b=11.25/a (from first equation)

c=36/b = 36a/11.25

ac=20

a * [36a / 11.25] = 20

solve for a =15/6

c= 36a/11.25 = 36(15/6) /11.25 = 8

ElectricPavlov Nov 3, 2019

#10**+1 **

ab = 11.25 ⇒ b = 11.25 / a (1)

ac = 20 ⇒ c = 20 / a (2)

bc = 36 (3)

Sub (1) and (2) into (3)

(11.25 /a ) (20 / a) = 36

225/ a^2 = 36 rearrange as

a^2 = 225/36 take the positive root

a = 15 / 6 = 5 / 2

So....using (2).....

c = 20 / ( 5/2) = 8

CPhill Nov 3, 2019

#11**+1 **

Really cool! Thanks CPhill! Man Im glad I found this math site

What do you mean by positive root.

Guest Nov 3, 2019

#12**+1 **

225 / 36 has two roots : (-15/6) and (15/6)

If we square both of these.....we get 225 /36

But.....since "a" is positive....we need 15 / 6 = 5 / 2

Does that make sense ???

CPhill
Nov 3, 2019

#13**+1 **

Oh yea! I remember the 2 roots thing from quadratic equations but I didnt know that one was a minus number. I remember some them had two plus numbers. How do you know which one to use if they are both plus numbers?

Guest Nov 3, 2019