You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?
Let's start by assigning a variable to represent the number of sodas you can buy. Let's use "s" for sodas.
To find the maximum number of sodas you can buy, we need to consider the total amount of money you have and the prices of the snacks.
The price of each soda is $2.50, the price of popcorn is $3.75, and you have $15 in total.
Since you want to buy a bag of popcorn as well, let's factor in its cost. The total cost of one bag of popcorn and "s" sodas can be represented as:
Total cost = cost of popcorn + (cost of soda x number of sodas)
The equation that models this situation is:
3.75 + (2.50s) ≤ 15
To find the maximum number of sodas, we need to solve this inequality:
3.75 + (2.50s) ≤ 15
Now, let's solve the inequality to find the maximum number of sodas you can buy.
3.75 + 2.50s ≤ 15
2.50s ≤ 15 - 3.75
2.50s ≤ 11.25
s ≤ 11.25 / 2.50
s ≤ 4.5
Since you cannot buy a fraction of a soda, the maximum number of sodas you can buy is 4.
To find the inequality that models the number of sodas you can buy, we need to consider the total cost of the items and the amount of money you have.
Let's assume the number of sodas you can buy is "x".
The cost of a bag of popcorn is $3.75.
The cost of x sodas would be $2.50 * x.
So, the total cost of x sodas and a bag of popcorn would be $2.50 * x + $3.75.
Since you have $15, the inequality that models the number of sodas you can buy would be:
$2.50 * x + $3.75 ≤ $15
To find the maximum number of sodas you can buy, we need to solve this inequality.
Subtracting $3.75 from both sides of the inequality, we get:
$2.50 * x ≤ $15 - $3.75
Simplifying, we have:
$2.50 * x ≤ $11.25
Now, divide both sides of the inequality by $2.50 to isolate "x":
x ≤ $11.25 / $2.50
x ≤ 4.5
Therefore, the maximum number of sodas you can buy in this situation is 4.
obviously,
2.50s + 3.75p ≤ 15
divide by .25
10s + 15p ≤ 60
2s + 3p ≤ 12
if you want to buy max sodas, then p = 0
s = 6
note 6 sodas will cost 6($2.5) or $15