Homework SourseFive postive integers when added four at a time give the sum
Five postive integers, when added four at a time, give the sums 119, 130, 134, 149, and 152. What is the largest of these five integers? Is the answer 52?
Solution
a +b + c+ d = 119 b+c+d +e = 130 c+d+e+a = 134 d+e+a+b = 149 e+a+b+c = 152 adding all we get, 4(a+b+c+d+e) = 684 a+b+c+d+e = 171 substituting eqn 1 in this we get e = 171-119 = 52 substituting eqn 2 in this we get a = 41 substituting eqn 3 in this we get b= 37 similarly , c= 22 and d = 19 Thus, the largest number is 52
