Number factor product

The product of two numbers we know. If we increase the first factor by 2 and decrease the second factor by two, the product increases by 4. How much does the product change if we decrease the first factor by 3 and increase the second factor by 3?

Final Answer:

s =  3

Step-by-step explanation:

$$\begin{gathered} x\cdot y=z \\ (x+2)(y-2)=z+4 \\ x\cdot y-4+2y-2x=z+4 \\ z-4+2y-2x=z+4 \\ 2y-2x=8 \\ y-x=4 \\ x=y-4 \\ y=x+4 \\ z=x\cdot y=x(x+4) \\ (x+3)(y-3)=xy-9+3y-3x=z-9+3y-3\cdot (y-4)=z-9+3y-3y+12 \\ (x+3)(y-3)=z-9+12=z+3 \\ s=3 \\ \text{ Verifying Solution: } \\ x=13 \\ y=x+4=13+4=17 \\ {z}_1=x\cdot y=13\cdot 17=221 \\ {z}_2=(x+2)\cdot (y-2)=(13+2)\cdot (17-2)=225 \\ {z}_3=(x+3)\cdot (y-3)=(13+3)\cdot (17-3)=224 \\ {s}_2=z_3-z_1=224-221=3 \\ {s}_2=s \end{gathered}$$

Try another example