Five children

Five children in a family are weighed, and their weights are recorded as follows: Dave weighs 46 kg. Dave and Ann weigh 84 kg. Ann and Mark weigh 74 kg. Mark and Carol weigh 50 kg. Eli, Ann, and Carol weigh 100 kg. Find the weight of each person.

Correct answer:

A =  38 kg
M =  36 kg
C =  14 kg
E =  48 kg

Step-by-step explanation:

$$\begin{gathered} D=46\text{kg} \\ A+D=84\text{kg} \\ A=84-D=84-46=38\text{kg} \end{gathered}$$

$$\begin{gathered} A+M=74\text{kg} \\ M=74-A=74-38=36\text{kg} \end{gathered}$$

$$\begin{gathered} M+C=50\text{kg} \\ C=50-M=50-36=14\text{kg} \end{gathered}$$

$$\begin{gathered} E+A+C=100 \\ E=100-A-C=100-38-14=48\text{kg} \end{gathered}$$

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