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Add up all 5 equations given below. What do you notice? Solve the system and find the values of a, b, c , d and e. b + c + d + e = 4 a + c + d + e = 5 a + b + d + e = 1 a + b + c + e = 2 a + b + c + d = 0

Weekly Problem 36 - 2008

Stage: 3 Short Challenge Level: Challenge Level:1

Call the baby's weight $b$, my weight $m$ and the nurse's weight $m$.

Then we know $$b+m=78 \; \text{kg}$$ $$n+b=69 \; \text{kg}$$ and $$m+n=137 \; \text{kg}$$
Adding the three equations together gives $$2b+2m+2n=284 \; \text{kg}$$ so dividing both sides by two gives us $$b+m+n=142 \; \text{kg}$$

This problem is taken from the UKMT Mathematical Challenges.

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