For this case we have the following variables:
x: Quantity of orange picks
y: Quantity of green picks
According to the statement, we have the following proportion:
[tex]\frac{2}{5}=\frac{x}{y}[/tex], that is:
[tex]5x = 2y[/tex]
If there are 21 picks, then:
[tex]x + y = 21[/tex]
So, we have two equations with two unknowns:
[tex]5x = 2y[/tex] ----> (1)
[tex]x + y = 21[/tex] ----> (2)
From (2):
[tex]x = 21-y[/tex]
Substituting x in (1):
[tex]5 (21-y) = 2y\\105-5y = 2y\\105 = 7y\\[/tex]
[tex]y = \frac{105}{7}\\y = 15[/tex]
Substituting[tex]y = 15[/tex] in (2) and clearing x, we have:
[tex]x + 15 = 21[/tex]
[tex]x = 21-15[/tex]
[tex]x = 6[/tex]
So, there are 6 orange picks
Answer:
6 orange picks
