Question

12) Lily is saving up to buy a cellphone. She needs to save at least $300 before she is able to buy the phone. Her grandfather gives her $40, and she earns $65 tutoring after school each week. Write an inequality for the number of weeks Lily will need to save to have at least $300. Make sure you write your inequality in the form of px + q > r (Make sure you choose the correct inequality symbol!) and solve. Show your work and explain your answer.
Inequality symbols in case you need: > < greater than or equal to, less than or equal to.
1 point: Correct inequality written in provided form.
1 point: Correct answer written as an inequality.
2 points: Showing work + explanation.
(4 points)

Answer 1

Let x = number of weeks Lily tutors.

"I need at least $300" gives the inequality:
65x + 40 ≥ 300
(65 dollars per week plus the $40 gift is at least $300)

Solve:
65x + 40 ≥ 300
65x ≥ 300 − 40
65x ≥ 260
x ≥ 260 ÷ 65
x ≥ 4

Check: after 4 weeks she has 65(4) + 40 = 260 + 40 = 300, which meets the requirement.

Answer: 65x + 40 ≥ 300, and x ≥ 4. Lily needs to save for at least 4 weeks.