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:
\(\frac{2}{5}=\frac{x}{y}\), that is:
\(5x = 2y\)
If there are 21 picks, then:
\(x + y = 21\)
So, we have two equations with two unknowns:
\(5x = 2y\) ----> (1)
\(x + y = 21\) ----> (2)
From (2):
\(x = 21-y\)
Substituting x in (1):
\(5 (21-y) = 2y\\105-5y = 2y\\105 = 7y\\\)
\(y = \frac{105}{7}\\y = 15\)
Substituting\(y = 15\) in (2) and clearing x, we have:
\(x + 15 = 21\)
\(x = 21-15\)
\(x = 6\)
So, there are 6 orange picks
Answer:
6 orange picks
