Rod cutting lengths

We want to cut a 90 cm long rod into two parts so that the longer part of the rod is 2 cm shorter than three times the shorter part. Determine the lengths of both parts of the rod.

Final Answer:

a =  67 cm
b =  23 cm

Step-by-step explanation:

$$\begin{gathered} a+b=90 \\ a=3b-2 \\ (3b-2)+b=90 \\ (3\cdot b-2)+b=90 \\ 4b=92 \\ b=\frac{92}{4}=23 \\ b=23 \\ a=3\cdot b-2=3\cdot 23-2=67\text{cm} \end{gathered}$$

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