Lala=rs 14,loal =rs 12,ola=rs 10 and oola=rs? What are the values of l , a and o

Question

The answer should be a single digit number

Answer 1

lala = oola(14)

loal = oola(12)

ola = oola(10)


Rewriting the equations:

a^2*l^2 = 14*a*l*o^2

a*l^2*o = 12*a*l*o^2

a*l*o = 10 * a*l*o^2


Cancelling:

a*l = 14*o^2 <--- divides by a*l

l = 12*o <---- divides by a*l*o

1 = 10 * o <--- divides by a*l*o




So o = 1/10

Plugging into second equation:

l = 12 (1/10) = 12/10 = 5/6

Plugging into first equation:

a*(5/6) = 14*(1/10)^2 = 14/100 = 7/50

a = 7/50*6/5 = 42/250 = 21/125 =(3*7)/ (5*5*5) <--- reduced to lowest terms

Next rs = oola = o^2*l*a = (1/10)^2*(5/6)*(21/125) = 105/(600*125) = 21/(600*25) = 7/(200*25) = 7/5000


Now we check the original equations:

lala = l^2*a^2 = (5/6)^2*(21/125)^2 = (5*5*21*21)/(6*6*125*125) = (7*7)/(2*2*25*25) = 49/2500
14rs = 14(7/5000) = (7*7)/2500 = 49/2500. So lala = 14rs.


ola = (1/10)(5/6)(21/125) = (5*21)/(10*6*125) = 7/(2*2*125) = 7/500
10rs = 10(7/5000) = 7/500. So ola = 10rs.

Answer 2

Hey, wait a minute. what figure pertains to this question (if any)?  what do all of these lower case letters mean? 

Is this algebra or is it geometry? Is capital L the same as l in Lala?  Please clarify!