A 2x2 grid is filled with numbers such that: (1). The product of the numbers in the left column is 1/42 and on the right column is 1/72. (2). The sum of the numbers in the top row is 7/24 and in the bottom row is 16/63. Let the top-left entry be a, the top-right entry be b, the bottom-left entry be c, and the bottom-right entry be d. Express ad+bc as a reduced fraction

Mathgenius Dec 2, 2018

#1**+1 **

We have

ac = 1/42 ⇒ c = 1 / (42a) (1)

bd = 1/72 ⇒ b = 1/(72d) (2)

a + b = 7/24 (3)

c + d = 16/63 (4)

42ac = 1

72bd = 1

24a + 24b = 7

63c + 63d = 16 this system is a little sticky to solve, but note that

a = (1/6) b = (1/8) c = (1/7) d = (1/9) make the system true

So ad + bc = (1/6)(1/9) + (1/8)(1/7) = (1/54) + (1/56) =

(54 + 56) / 3024

110/ 3024 =

55 / 1512

CPhill Dec 2, 2018