Question

Hector wants to buy bags of popcorn and bags of peanuts. The price of each bag of popcorn is $1 and the price of each bag of peanuts is $2. Hector wants to buy c bags of popcorn and y bags of peanuts. He doesn't want to buy more than 8 bags in total. He has at most $14 to spend. How many bags of popcorn and bags of peanuts can Hector buy?

Answer 1

Hector can buy various combinations of popcorn and peanuts as long as he does not exceed 8 bags in total and spends at most $14, considering the price of popcorn is $1 and peanuts is $2.

Step-by-step explanation:

Hector’s problem involves finding a solution to a consumer budget constraint in Mathematics. Given that a bag of popcorn costs $1 and a bag of peanuts costs $2, Hector wants to buy c bags of popcorn and y bags of peanuts without exceeding 8 bags in total or spending more than $14.

The constraints can be written as two inequalities: c + y ≤ 8 (for the quantity of bags) and $1c + $2y ≤ $14 for the amount to spend. To solve this, we will consider various combinations of c and y that satisfy both inequalities.