Answer:
The number of skateboards of each color is 11 and 4
Explanation:
Let x represent blue skateboards and
y represent red skateboards.
From the question, the total number of skateboards is 15, that is,
x + y = 15 ...... (1)
and their product is 44, that is,
xy = 44 ...... (2)
From equation (1),
x + y = 15
We can write that
x = 15 - y ...... (3)
Substitute this into equation (2)
xy = 44
(15-y)y = 44
15y -y² = 44
Then,
y² - 15y + 44 = 0
Solve quadratically
y² -4y -11y + 44 = 0
y(y-4) -11(y-4) = 0
(y-11)(y-4) = 0
y-11 = 0 OR y-4 = 0
y = 11 OR y = 4
Put the values of y into equation (3) for x
x = 15 - y
When y = 11
x = 15 - 11
x = 4
and when y = 4
x = 15 -4
x = 11
(4,11) and (11,4)
It is either 4 blue and 11 red skateboards OR 11 blue and 4 red skateboards.
Hence, the number of skateboards of each color is 11 and 4.