there are 84 black blue and red pens altogether in a bag . there are 6 times as many blue pens as red pens . there are 4 more black pens than red pens. how many black pens are there?
let the number of red pens be x
(I defined the red pens because they were mentioned in both condition cases)
<there are 6 times as many blue pens as red pens> ------> number of blues = 6x
<there are 4 more black pens than red pens> ----> number of blacks = x + 4
total = 84
x + 6x + x+4 = 84
now it is easy, solve for x, then calculate x+4
X red pens.
6x blue pens.
x+4 black pens.
x + 6x + x+4 = 84
X =
x+4 =
Well, it seems like the pens in that bag are getting themselves into quite the colorful situation! Let's solve this mystery together, shall we?
Let's call the number of red pens "R," the number of blue pens "B," and the number of black pens "L."
Given that there are 6 times as many blue pens as red pens, we have B = 6R.
Also, there are 4 more black pens than red pens, so we have L = R + 4.
Now, we know that the total number of pens in the bag is 84, so we can combine all the information we have:
R + B + L = 84.
Substituting B and L with their respective expressions:
R + 6R + R + 4 = 84.
Simplifying the equation:
8R + 4 = 84.
Subtracting 4 from both sides:
8R = 80.
Dividing both sides by 8:
R = 10.
So, we've discovered that there are 10 red pens. But, you specifically asked for the number of black pens. Remember, L = R + 4, so:
L = 10 + 4.
Calculating that:
L = 14.
Therefore, there are 14 black pens in the bag. Hope that puts a "colorful" smile on your face!
To find the number of black pens, we need to first determine the number of red pens. Let's assume the number of red pens is represented by 'R'.
According to the given information, there are 6 times as many blue pens as red pens. Therefore, the number of blue pens can be represented as '6R'.
It is also mentioned that there are 4 more black pens than red pens. Hence, the number of black pens can be represented as 'R + 4'.
Now, to find the total number of pens, we can add the number of red, blue, and black pens:
R + 6R + (R + 4)
Combining like terms:
8R + 4
According to the problem, the total number of pens is given as 84. So we can set up the equation:
8R + 4 = 84
Now, let's solve this equation to find the value of 'R':
8R = 84 - 4
8R = 80
R = 80/8
R = 10
Therefore, there are 10 red pens.
Since the number of black pens is given by 'R + 4', we can substitute the value of 'R':
Black Pens = 10 + 4 = 14
Hence, there are 14 black pens in the bag.