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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

 Dec 2, 2018
 #1
avatar+100519 
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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

 

 

 

 

cool cool cool

 Dec 2, 2018

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