Respuesta :
Answer:
The red pens are 168.
Step-by-step explanation:
Given:
In a box of pens, 2/7 of them are red. of the remaining pens 1/6 of them are blue and the rest are black. there are 280 more black pens than blue pens.
Now, to find the red pens in the box.
Let the total pens be [tex]x[/tex].
Red pens be [tex]\frac{2}{7} of x =\frac{2x}{7}[/tex]
Remaining pens = [tex]x-\frac{2x}{7} =\frac{5x}{7}[/tex]
So, blue pens = [tex]\frac{1}{6} of \frac{5x}{7} =\frac{5x}{42}[/tex]
Now, black pens = [tex]x[/tex]-(blue +red)
Black pens = [tex]x-\frac{2x}{7}+\frac{5x}{42}[/tex]
According to question:
Black pens = Blue pens + 280
[tex]x-\frac{2x}{7}+\frac{5x}{42}[/tex][tex]=\frac{5x}{42}+280[/tex]
[tex]x-\frac{17x}{42}=\frac{5x}{42}+280[/tex]
[tex]x-\frac{22x}{42}=280[/tex]
[tex]20\frac{x}{42}=280[/tex]
[tex]x=\frac{280\times 42}{20}[/tex]
On solving we get:
[tex]x=588[/tex]
So, red pens = [tex]\frac{2x}{7}=\frac{2\times 588}{7}[/tex]
=[tex]168[/tex].
Therefore, the red pens are 168.
