37 pens

Thirty-seven pens and 53 pencils together cost 95.5 USD, while 53 pens and 37 pencils together cost 111.5 USD. Find the cost of a pen and a pencil.

Correct answer:

a =  1.65 USD
b =  0.65 USD

Step-by-step explanation:

$$\begin{gathered} 37a+53b=95.5 \\ 53a+37b=111.5 \\ 37\cdot a+53\cdot b=95.5 \\ 53\cdot a+37\cdot b=111.5 \\ 37a+53b=95.5 \\ 53a+37b=111.5 \\ Pivot:Row1\leftrightarrow Row2 \\ 53a+37b=111.5 \\ 37a+53b=95.5 \\ Row2-\frac{37}{53}\cdot Row1\to Row2 \\ 53a+37b=111.5 \\ 27.17b=17.66 \\ b=\frac{17.66037736}{27.16981132}=0.65 \\ a=\frac{111.5-37b}{53}=\frac{111.5-37\cdot 0.65}{53}=1.65=1.65\text{USD} \\ a=\frac{33}{20}=1.65 \\ b=\frac{13}{20}=0.65 \end{gathered}$$

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