Finding the weight of 5 children when data given is weight in pairs.

Question

5 children find a scale but is does not read below 75 pounds, so they weigh themselves in pairs. Their weights in pairs are 80, 82, 83, 84, 85, 86, 87, 88, 90, and 91. What is the weight of each child?

Answer 1

A+B = 80

A+C = 82

A+D = 83

A+E = 84

B+C=85

B+D=86

B+E = 87

C+D = 88

C+E = 90

D+E = 91

eq10 - eq9 ---> D-C = 1

C+D = 88 <-- eq 8

adding them together: 2D = 89

D = 44.5

C = 43.5

eq #2: A+C = 82

A + 43.5 = 82

A = 82 - 43.5 = 38.5

1st equation A+B = 80

38.5 + B = 80

B = 80 - 38.5 = 41.5

9th equation: C+E=90

43.5 + E = 90

E = 90 - 43.5 = 46.5