each man in a gang of 100 investors has investments ineither equities or securities or both. Exactly 2525 of the investors in equities haveinvestments in securities, exactly 4040 of the investorsin securities have investments inequities. How many have investmentsin equities?	Choose the correct choice from the following options:
A) 70	B) 80	C) 90	D) 100	E) 120
The investors can be categorized into three groups:   (1) Those who have investments in equities only.   (2) Those who have investments in securities only.   (3) Those who have investments in both equities and securities.   Let xx, yy, and zz denote the number of people in the respective categories. Since the total number of investors is 110, we have   x+y+z=110x+y+z=110 ------------- (1)   Also,   The number of people with investments in equities is x+zx+z and   The number of people with investments in securities is y+zy+z.   Since exactly 25%25% of the investors in equities have investments in securities, we have the equation   25100×(x+z)=z25100×(x+z)=z   25100×x=25100×z25100×x=25100×z   x=3zx=3z ------------------- (2)   Since exactly 40%40% of the investors in securities have investments in equities, we have the equation   40100×(y+z)=z40100×(y+z)=z   (y+z)=5z2(y+z)=5z2   y=3z2y=3z2   Substituting equations (2) and (3) into equation (1) yields   3z+3z2+z=1103z+3z2+z=110   11z2=11011z2=110   z=110×211=20z=110×211=20   Hence, the number of people with investments in equities is:   x+z=3z+z=3×20+20=60+20x+z=3z+z=3×20+20=60+20= 
<gadget id="calculator">60+20</gadget>
<output>80</output>
80   80
<result>B</result>
each man in a gang of 100 investors has investments ineither equities or securities or both. Exactly 2525 of the investors in equities haveinvestments in securities, exactly 4040 of the investorsin securities have investments inequities. How many have investmentsin equities?