Final answer:
The equation to model the scenario of spending $100 on drinks and popcorn for a movie outing is $100 = $5 × Qdrinks + $7 × Qpopcorn. This can be rearranged into a linear equation, representing the budget constraint for the purchase of drinks and popcorn.
Step-by-step explanation:
To write an equation that models the given situation of spending $100 on movie outing with friends, taking into account the cost of drinks and popcorn, you could set up the following budget constraint equation:
Budget = P1 × Q1 + P2 × Q2
Where:
- Budget is the total amount of money available to spend, $100 in this case.
- P1 is the price of one drink, which is $5.
- Q1 is the quantity of drinks.
- P2 is the price of one popcorn, which is $7.
- Q2 is the quantity of popcorn.
Therefore, the equation modeling the scenario would be:
$100 = $5 × Qdrinks + $7 × Qpopcorn
If we use a little algebra, we can rearrange this into the equation of a line:
y = mx + b, where y represents the total cost (here capped at $100), m and x represent the price and quantity of one item, and b is the constant representing the cost of the other item times its quantity.