Question

Gloria set aside $100 to buy school lunches for the year. Each school lunch costs $2. The inequality 100 - 2x < 40 represents the number of lunches she can buy while staying within her budget. Solve for x.

a) x > 30
b) x < 30
c) x = 30
d) x ≥ 30

Answer 1

To solve the inequality 100 - 2x < 40, you subtract 100 from both sides and divide by -2, which gives x > 30. This means Gloria can purchase more than 30 school lunches while staying under her $100 budget and having less than $40 leftover.

Step-by-step explanation:

The inequality 100 - 2x < 40 represents the condition where Gloria wishes to ensure she has less than $40 remaining after buying school lunches. To solve for x, which represents the number of lunches Gloria can purchase, we start by subtracting 100 from both sides of the inequality:

100 - 100 - 2x < 40 - 100

-2x < -60

Next, we divide both sides by -2, remembering to reverse the inequality because we are dividing by a negative number:

-2x / -2 > -60 / -2

x > 30

Thus, the correct answer is x should be greater than 30 lunches to stay within her budget, that is, Gloria can buy more than 30 school lunches and still have less than $40 remaining.