A box contains blue and purple pens. There are 6 less than triple the number of blue pens as purple pens. A blue pen costs 20 cents and a purple pen cost 35 cents. The total value of all the pens is $37.90. How many of each colour pen is their?
p = 3b-6
20b+35p = 3790
Now just solve for b and p to see how many of each there are.
To solve this problem, we can set up a system of equations based on the information given.
Let's assume the number of blue pens is "b" and the number of purple pens is "p".
According to the first statement, the number of blue pens is 6 less than triple the number of purple pens:
b = 3p - 6 (Equation 1)
According to the second statement, the cost of a blue pen is 20 cents and the cost of a purple pen is 35 cents:
0.20b + 0.35p = 37.90 (Equation 2)
Now, we have a system of two equations with two variables. We can solve this system to find the values of "b" and "p".
First, let's substitute the value of b from Equation 1 into Equation 2:
0.20(3p - 6) + 0.35p = 37.90
Now, we can simplify this equation and solve for p:
0.60p - 1.20 + 0.35p = 37.90
0.95p = 39.10
p = 39.10 / 0.95
p ≈ 41.16
The value of p is approximately 41.16. Since the number of pens must be a whole number, we can round it to the nearest whole number. Therefore, p ≈ 41.
Now we can substitute the value of p = 41 into Equation 1 to find the number of blue pens:
b = 3(41) - 6
b = 123 - 6
b ≈ 117
The value of b is approximately 117.
So, there are approximately 117 blue pens and 41 purple pens.