Answer:
Alec sold 26 bags of butter popcorn and 14 bags of caramel popcorn
Step-by-step explanation:
Let
x------> the number of bags of butter popcorn sold
y------> the number of bags of caramel popcorn sold
we know that
[tex]x+y=40[/tex] -----> equation A
[tex]5x+6.5y=221[/tex] -----> equation B
Solve the system of equations by graphing
see the attached figure
The solution is the point (26.14)
therefore
Alec sold 26 bags of butter popcorn and 14 bags of caramel popcorn
Answer: The boy sold 26 bags of butter popcorn and 14 bags of caramel popcorn.
Step-by-step explanation: Given that the boy scouts are selling two types of popcorn as part of a fundraiser, butter and caramel.
Butter popcorn sells for $5 per bag and caramel popcorn sells for $6.50 per bag. Till now, Alec has sold 40 total bags and raised $221.
We are to find the number of bags he has sold for each type of popcorn.
Let a and b represents the number of bags of butter popcorn and caramel popcorn that the boy sold.
Then, according to the given information, we have
[tex]a+b=40~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5a+6.5b=221~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 5, we have
[tex]5a+5b=200~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (iii) from equation (ii), we get
[tex](5a+6.5b)-(5a+5b)=221-200\\\\\Rightarrow 1.5b=21\\\\\Rightarrow b=\dfrac{21}{1.5}\\\\\Rightarrow b=14.[/tex]
From equation (i), we get
[tex]a+b=40\\\\\Rightarrow a+14=40\\\\\Rightarrow a=40-14\\\\\Rightarrow a=26.[/tex]
Thus, the boy sold 26 bags of butter popcorn and 14 bags of caramel popcorn.
