Bent scale

Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the needle on the scale was bent. How much did they really weigh?

Correct answer:

M =  57 kg
S =  59 kg

Step-by-step explanation:

$$\begin{gathered} M+x=52 \\ S+x=54 \\ M+S+x=111 \\ M+x=52 \\ S+x=54 \\ M+S+x=111 \\ Row3-Row1\to Row3 \\ M+x=52 \\ S+x=54 \\ S=59 \\ Row3-Row2\to Row3 \\ M+x=52 \\ S+x=54 \\ -x=5 \\ x=\frac{5}{-1}=-5 \\ S=54-x=54+5=59 \\ M=52-x=52+5=57=57\text{kg} \\ M=57 \\ S=59 \\ x=-5 \end{gathered}$$

$S=59=59\text{kg}$

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