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:
[tex]x + y = 130\\2x + 3y = 310[/tex]
We multiply the first equation by -2:
[tex]-2x-2y = -260[/tex]
We have the following equivalent system:
[tex]-2x-2y = -260\\2x + 3y = 310[/tex]
We add the equations:
[tex]-2x + 2x-2y + 3y = -260 + 310\\y = 50[/tex]
We look for the value of the variable "x":
[tex]x = 130-y\\x = 130-50\\x = 80[/tex]
Answer:
They sold 80 small cookies and 50 large cookies
