Four children weigh themselves in pairs and take the average mass of each pair. The average mass of the six pairs are: 47kg, 50kg, 51kg, 53kg, 54kg, 57kg.
Find the mass of the heaviest child.
I'm finding this hard to calculate the heaviest child. I know the heaviest two weigh 114kg and next heaviest two 108kg and the difference is 6kg, but can't work out a logical way to find the heaviest weight.
Any help would be greatly appreciated!
Let the 4 kids be: A, B, C, D
A+B=2*47, A+C=2*50, A+D=2*51, B+C=2*53, B+D =2*54, C+D=2*57, solve for A, B, C, D
Solve the following system:
{A + B = 94 | (equation 1)
A + C = 100 | (equation 2)
B + C = 106 | (equation 3)
Subtract equation 1 from equation 2:
{A + B+0 C = 94 | (equation 1)
0 A - B + C = 6 | (equation 2)
0 A+B + C = 106 | (equation 3)
Add equation 2 to equation 3:
{A + B+0 C = 94 | (equation 1)
0 A - B + C = 6 | (equation 2)
0 A+0 B+2 C = 112 | (equation 3)
Divide equation 3 by 2:
{A + B+0 C = 94 | (equation 1)
0 A - B + C = 6 | (equation 2)
0 A+0 B+C = 56 | (equation 3)
Subtract equation 3 from equation 2:
{A + B+0 C = 94 | (equation 1)
0 A - B+0 C = -50 | (equation 2)
0 A+0 B+C = 56 | (equation 3)
Multiply equation 2 by -1:
{A + B+0 C = 94 | (equation 1)
0 A+B+0 C = 50 | (equation 2)
0 A+0 B+C = 56 | (equation 3)
Subtract equation 2 from equation 1:
{A+0 B+0 C = 44 | (equation 1)
0 A+B+0 C = 50 | (equation 2)
0 A+0 B+C = 56 | (equation 3)
Collect results: A = 44, B = 50, C = 56
C + D =2 x 57
56 + D = 114
D = 114 - 56 = 58
A = 44 and B = 50 and C = 56 and D=58 - which is the heaviest child.