Three cards are lined up on a table. each card has a letter printed on one side
and a positive number printed on the other side. one card has an r printed on
it, one card has a g printed on it, and one card has a b printed on it. the
number side of each card is facedown on the table. the following is known about
the three concealed numbers:

(i) the product of the number on the card with an r and the number on the
card with a g equals the number on the card with a b;
(ii) the product of the number on the card with a g and the number on the card
with a b is 180; and
(iii) five times the number on the card with a b equals the number on the card
with a g.

determine the product of the numbers on the three cards.

Product of the numbers on three cards is 36 .

Step-by-step explanation:

Let the numbers on the cards with R , G , B respectively be, x , y and z.

Then, according to the question, we get the following 3 equations,

xy = z ----------- (1)

yz = 180 ------------(2)

5z = y ------------(3)

so, from (3) we get, z = y/5 -----------(4)

Putting the value of z from (4) in (2) we get,

⇒ y = 30 [since, y > 0] ------------(5)

So, from (5) and (3) we get,

z = 30/5 = 6 ------------------(6)

so, from (1) we get, xyz =

                                      =

                                      = 36

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: