Three cards are lined up on a table. Each card has a letter printed on one sideand a positive number printed on the other side. One card has an R printed onit, one card has a G printed on it, and one card has a B printed on it. Thenumber side of each card is facedown on the table. The following is known aboutthe three concealed numbers:(i) the product of the number on the card with an R and the number on thecard 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 cardwith a B is 180; and(iii) five times the number on the card with a B equals the number on the cardwith a G.Determine the product of the numbers on the three cards.
Accepted Solution
A:
Answer: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, [tex]y^{2} = 900[/tex]⇒ y = 30 [since, y > 0] ------------(5)So, from (5) and (3) we get,z = 30/5 = 6 ------------------(6)so, from (1) we get, xyz = [tex]z^{2}[/tex] = [tex]6^{2}[/tex] = 36