Respuesta :
Answer:
6 or 9
Step-by-step explanation:
Let the number of green pens =x
There are three more red pens, therefore:
The number of red pens =x+3
Total Number of pens =x+x+3=2x+3
The probability that sheila will take two pens of the same color = [tex]\frac{17}{35}[/tex]
Therefore, we have that:
[tex]\text{P(two red pens)}=\dfrac{x+3}{2x+3} \times \dfrac{x+2}{2x+2}\\\\P(RR)=\dfrac{(x+3)(x+2)}{(2x+3)(2x+2)}[/tex]
[tex]P$(two green pens$)=\dfrac{x}{2x+3} \times \dfrac{x-1}{2x+2}\\\\P(GG)=\dfrac{x(x-1)}{(2x+3)(2x+2)}[/tex]
Therefore, the probability that sheila will take two pens of the same color
=P(RR)+P(GG)
[tex]\dfrac{(x+3)(x+2)}{(2x+3)(2x+2)}+\dfrac{x(x-1)}{(2x+3)(2x+2)}=\dfrac{17}{35}\\\dfrac{(x+3)(x+2)+x(x-1)}{(2x+3)(2x+2)}=\dfrac{17}{35}\\[/tex]
Cross multiply
[tex]35[(x+3)(x+2)+x(x-1)]=17[(2x+3)(2x+2)]\\35[x^2+3x+2x+6+x^2-x]=17[4x^2+4x+6x+6]\\35[2x^2+4x+6]=17[4x^2+10x+6]\\70x^2+140x+210=68x^2+170x+102\\70x^2-68x^2+140x-170x+210-102=0\\2x^2-30x+108=0[/tex]
Factorizing, we have:
[tex]2(x-6)(x-9)=0\\x-6=0$ or $x-9=0\\x=6$ or 9[/tex]
Therefore, the two different numbers of green pens that could be in the box are 6 or 9.
