Question 333707: In a group of five friends, the sums of the ages of each group of four of them are 124, 128, 130, 136, and 142. What is the age of the youngest?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! In a group of five friends, the sums of the ages of each group of four of them are 124, 128, 130, 136, and 142. What is the age of the youngest?
Let the five ages be A, B, C, D, and E.
A + B + C + D = 124
A + B + C + E = 128
A + B + D + E = 130
A + C + D + E = 136
B + C + D + E = 142
We consider that as this system, putting in all the
understood 1's and 0's
1A + 1B + 1C + 1D + 0E = 124
1A + 1B + 1C + 0D + 1E = 128
1A + 1B + 0C + 1D + 1E = 130
1A + 0B + 1C + 1D + 1E = 136
0A + 1B + 1C + 1D + 1E = 142
Now we make the augmented matrix:
Using my TI-84 I get for the rref of that matrix:
A=23, B=29, C=35, D=37, E=41.
The youngest age is A, which is 23.
Edwin
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