Question

Lily wants to save at least $325 for a new bicycle by working over spring break. She earns $12 per hour babysitting and $18 per hour working at the coffee shop. Lily has no more than 20 hours to work over break. Let x represent the hours babysitting and y represent the hours working at the coffee shop. Select all the inequalities that represent the situation.

1) 12x + 18y > 325
2) 18x + 12y ≥ 325
3) x + y ≤ 20
4) x + y = 20
5) 12x + 18y ≥ 325

Answer 1

Lily needs to save at least $325 for a bicycle, earning $12/h babysitting and $18/h at a coffee shop, with a maximum of 20 hours to work. The inequalities representing the situation are 12x + 18y ≥ 325 and x + y ≤ 20.

Step-by-step explanation:

Lily is trying to save at least $325 for a new bicycle by working over spring break. She can earn money two ways: $12 per hour babysitting (x) and $18 per hour working at a coffee shop (y). With no more than 20 hours to work over the break, we can create two inequalities to represent her situation. First, Lily's earnings need to be at least $325, so the first inequality will be 12x + 18y ≥ 325 to represent that combined earnings from both jobs should be greater than or equal to $325. Second, the total hours worked at both jobs cannot exceed 20 hours, so the second inequality is x + y ≤ 20 to ensure that the total number of hours worked doesn't surpass the time she has available.