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Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?

 Aug 13, 2020
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Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020.
If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?

 

\(\text{ Let first number $=n_1$} \\ \text{ Let second number $=n_2$}\)

 

\(\begin{array}{|lrcll|} \hline (1) & (n_1+1)(n_2-1) &=& n_1n_2 + 2020 \\ & n_1n_2-n_1+n_2-1 &=& n_1n_2 + 2020 \\ & -n_1+n_2-1 &=& 2020 \\ & \mathbf{ -n_1+n_2 } &=& \mathbf{ 2021 } \\ \hline (2) & (n_1-1)(n_2+1) &=& n_1n_2 + x \\ & n_1n_2+n_1-n_2-1 &=& n_1n_2 + x \\ & n_1-n_2-1 &=& x \\ & \mathbf{ n_1-n_2-1 } &=& \mathbf{ x } \\ \hline (1)+(2): & -n_1+n_2 + n_1-n_2-1 &=&2021 +x \\ & -1 &=&2021 +x \\ & x &=& -2021 -1 \\ & \mathbf{x} &=& \mathbf{-2022} \\ \hline \end{array}\)

 

The value of the product decreases by 2022

 

laugh

 Aug 13, 2020

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