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# Algebra

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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 7, and the second one increases by 7, what value does the product decrease?

Oct 11, 2021

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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 7, and the second one increases by 7, what value does the product decrease?

let the numbers be x and y   and let the product decrease by k

$$(x+1)(y-1)=xy+2020\\ xy-x+y-1=xy+2020\\ -x+y-1=2020\\ y-x=2021\qquad (1)$$

$$(x-7)(y+7)=xy - k\\ xy+7x-7y-49=xy - k\\ 7x-7y-49= - k\\ 7(x-y)-49=-k\\ k=49-7(x-y)\\ k=49-7*-2021\\ k=49+7*2021\\ k=14196$$

it is up to the asker to check that the answer is correct.

Oct 11, 2021