Find the average of the 4 cards

Question

Take away card A. The sum of the remaining 3cards is 32. Take away card B. The sum of the remaining 3cards is 37. Take away card C. The sum of the remaining 3cards is 34. Take away card D. The sum of the remianing 3 cards is 29. 

Answer 1

B+C+D = 32

A+C+D = 37

A+B+D = 34

A+B+C = 29

 

Subtracts equation 2 from equation 1: A-B = 5 ---> A = B + 5

Subtracts equation 3 from equation 2: C - B = 3 ---> C = B + 3 

 

Subtracts equation 4 from equation 1: D- A = 3 --> D = A + 3 = (B+5)+3 = B + 8

 

A + B + C + D = (B+5)+B + (B + 3) + (B + 8) = 4B + 16

 

But when you take away card B from the 4 cards the sum is 37.

SO 4B +16 - B = 37

        3b + 16 = 37

      3b = 21    

         b = 7

 

a=12

c=10

d=15

 

The total is 44.

THe average is 44/4=11.