Need help please! I just need help with creating an inequality and solving it.
Ethen considers some fundraisers for the upcoming year. He looks at data from the first fundraiser the club did last year. The club sold a variety of snacks last year. The numbers of snacks sold are shown in the table.
Type of snack Number sold
Energy bars : 194
Baked chips: 200
Organic treats: 235
Whole grain crackers: 78
The club sold the snacks for $3 each. The club gets half of this amount as profit. The club also gets a bonus of $100 for any snack when it sells at least 200 of that snack. Last year’s data on sales are shown in the table.
(b) Write an inequality to show how many snacks of one type would need to be sold to earn a profit of at least $500. Support your inequality with an explanation
Let x = number of snacks
1.5x + 100 ≥ 500
Can you give the explanation?
To write an inequality that represents the number of snacks that need to be sold in order to earn a profit of at least $500, we need to consider the following information:
1. The club sold the snacks for $3 each.
2. The club gets half of this amount as profit.
3. The club gets a bonus of $100 for any snack when it sells at least 200 of that snack.
Let's break down the components of the inequality:
Let x represent the number of snacks of one type that need to be sold.
The profit per snack sold is $3 / 2 = $1.5.
So, the total profit for x snacks sold would be 1.5x.
If x is at least 200, then the bonus of $100 would be added to the total profit.
Therefore, the total profit for x snacks sold when x is at least 200 would be 1.5x + $100.
To earn a profit of at least $500, we can set up the inequality:
1.5x + $100 ≥ $500
Simplifying the equation further:
1.5x ≥ $500 - $100
1.5x ≥ $400
Dividing both sides of the inequality by 1.5, we obtain:
x ≥ $400 / 1.5
x ≥ 266.67
Since the number of snacks sold must be a whole number, we can round up to the nearest whole number:
x ≥ 267.
Therefore, the inequality that represents the number of snacks that need to be sold in order to earn a profit of at least $500 is:
x ≥ 267.