Question

Ethan has a hot dog cart. His hot dogs sell for $3.50 each. He has sold $28 worth of hot dogs so far today. Ethan wants his hot dog sales to be more than $70 today. Write and solve an inequality to represent the number of hot dogs Ethan still needs to sell. Show your work. Then describe the solution set in terms of the whole number of hot dogs Ethan needs to sell.

Answer 1

Let's assume that Ethan still needs to sell x hot dogs to reach his goal of selling more than $70 worth of hot dogs today.

The inequality to represent the number of hot dogs Ethan still needs to sell is:

3.5x + 28 > 70

Now, we can solve for x as follows:

3.5x + 28 > 70
3.5x > 70 - 28
3.5x > 42
x > 42/3.5
x > 12

Therefore, Ethan needs to sell more than 12 hot dogs to reach his goal of selling more than $70 worth of hot dogs today.

The solution set in terms of the whole number of hot dogs Ethan needs to sell is {13, 14, 15, ...}. Since we cannot sell a fractional part of a hot dog, we need to round up to the nearest whole number. Thus, Ethan needs to sell at least 13 hot dogs.