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, and describe the solutions.
Let's say Lily will need x weeks to save at least $300.
She receives an additional $40 from her grandfather each week, so she earns $65 tutoring plus $40 from her grandfather, which gives her a total of $65 + $40 = $105 per week.
Therefore, the inequality for the number of weeks Lily will need to save to have at least $300 is:
105x ≥ 300.
The solutions for this inequality are any positive integer values of x that satisfy the inequality. Since x represents the number of weeks, the solutions will be whole numbers greater than or equal to the least number of weeks needed. In this case, Lily needs at least x = 3 weeks to have at least $300 because 105 * 3 = 315, but she does not have enough money in 2 weeks (105 * 2 = 210). Therefore, the solutions for x will be x = 3, 4, 5, 6,... and so on.
can i get a equation
Certainly! To write an equation instead of an inequality, we can write the equation for the exact amount Lily will have after x weeks to be at least $300.
Let's say the amount Lily saves after x weeks is A (in dollars). We are given that she starts with $40 from her grandfather and earns $65 tutoring each week.
Therefore, the equation becomes:
A = 40 + 65x.
Here, A represents the amount Lily saves after x weeks. As mentioned earlier, we want A to be equal to or greater than $300.