Ms.Franco has many pens.1/3 of her pens are blue.1/2 of her pens are black and the rest are all other colors.There were 5 more black pens than blue pens.How many pens were not black or blue?
To find the number of pens that were not black or blue, we need to first determine the number of blue and black pens.
Let's say that the total number of pens Ms. Franco has is represented by "x".
Given:
1/3 of her pens are blue, so the number of blue pens is (1/3) * x = x/3.
1/2 of her pens are black, so the number of black pens is (1/2) * x = x/2.
There are 5 more black pens than blue pens, so the number of black pens is x/3 + 5.
Since the blue pens are x/3, and the black pens are x/3 + 5, we can set up the equation:
x/3 + 5 = x/2
To solve this equation, first, multiply both sides by 6 to get rid of the denominators:
2(x/3 + 5) = 6(x/2)
2x/3 + 10 = 3x
Next, subtract 2x/3 from both sides to isolate the x term:
2x/3 + 10 - 2x/3 = 3x - 2x/3
10 = 3x - 2x/3
Multiply both sides by 3 to get rid of the denominator:
10 * 3 = 3x - 2x
30 = x
So, Ms. Franco has a total of 30 pens.
Now, to find the number of pens that were not black or blue, we subtract the sum of blue (x/3) and black (x/3 + 5) pens from the total number of pens (30):
30 - (x/3 + x/3 + 5) = 30 - (2x/3 + 5)
= 30 - 2x/3 - 5
= 30/1 - 2x/3 - 5/1
= (90 - 2x - 15)/3
= (75 - 2x)/3
Therefore, the number of pens that were not black or blue is (75 - 2x)/3. Substitute x = 30 into the equation to find the final answer.