It is true that (x+2)(x+3) = x2 +5x + 6
For this case we can propose a system of equations:
x: Let the variable that represents the number of small cookies
y: Let the variable that represents the number of large cookies
According to the statement we have:
We multiply the first equation by -2:
We have the following equivalent system:
We add the equations:
We look for the value of the variable "x":
Answer:
They sold 80 small cookies and 50 large cookies
The empirical probability of a 4 or 5 is
(count of outcome = 4 or 5)/(count of all outcomes) = (44 +40)/240 = 7/20
The problem statement asks you to assume the outcomes will remain in this proportion going forward. That is, the number of outcomes (n) of 4 or 5 in the next 60 rolls of the number cube is expected to satisfy
7/20 = n/60
Multiplying that by 60 gives
n = 60*(7/20) = 21
Selection D is appropriate.
21 is the length of the rectangle