Just add another 100?
Algebra
Level
3
I have 2 numbers whose product is 567.
If I add 2 to each of these numbers and multiply, then the new product becomes 667.
If I add 2 to each of the numbers one more time and multiply, then what is the value of this latest product?
The answer is 775.
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1 solution
if we let x and y be the 2 original numbers, the 2 equations given are xy=567 and (x+2)(y+2)=667.
(x+2)(y+2)=xy+2x+2y+4= 2x+2y+567+4=667
2(x+y)=96, meaning x+y=48.
(x+4)(y+4)=xy+4x+4y+16=567+4(x+y)+16=567+192+16= 775