+188 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
+128407 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
