anonymous
  • anonymous
the product of two numbers is 100. if one decreased by 5 and the other increased by 1, the product is still 100. how do i find the numbers?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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ganeshie8
  • ganeshie8
Let the two numbers be \(x\) and \(y\)
ganeshie8
  • ganeshie8
Can you set up equations based on given info ?
anonymous
  • anonymous
xy= 100 (x-5)(y+1)=100 I'm not sure where to go from there. I set them equal to each other, but that didn't work

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More answers

ganeshie8
  • ganeshie8
Your equations look good. Try eliminating one variable by substitution
ganeshie8
  • ganeshie8
\(xy= 100 \implies y = 100/x\) plug this in second equation
ganeshie8
  • ganeshie8
\((x-5)(\frac{100}{x}+1)=100\)
ganeshie8
  • ganeshie8
\((x-5)(\frac{100+x}{x})=100\)
ganeshie8
  • ganeshie8
\((x-5)(100+x)=100x\)
ganeshie8
  • ganeshie8
expand the left hand side you will see a quadratic equation which can be solved using quadratic formula
anonymous
  • anonymous
x=-20 or x= 25. I understand it now. Thanks! Does the equation also work if I substitute it after I expand the binomials?
anonymous
  • anonymous
I see that it does work. I did that in the beginning but I made an error somewhere, so I couldn't solve it. Thanks again.
ganeshie8
  • ganeshie8
np :)

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