Question

Lly 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. Lly 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.

A) 12x+18y≥325
B) 12x+18y≤325
C) x+y≤20
D) x≥0
E) y≥0

Answer 1

The inequalities that represent Lly's situation of saving at least $325 by working over spring break are A) 12x + 18y ≥ 325, C) x + y ≤ 20, D) x ≥ 0, and E) y ≥ 0.

Step-by-step explanation:

Lly wants to save at least $325 for a new bicycle by working over spring break, earning different wages from babysitting and working at a coffee shop. To represent this situation in inequalities, we must consider the wages per hour for each job, the total amount she wants to save, and the maximum hours she can work over break. Let x represent the hours babysitting and y represent the hours working at the coffee shop.

• 12x + 18y ≥ 325: This inequality shows that the total money earned from both jobs should be at least $325.
• x + y ≤ 20: Lly cannot work more than 20 hours in total over the spring break.
• x ≥ 0: The hours spent babysitting cannot be negative.
• y ≥ 0: The hours spent working at the coffee shop cannot be negative.

Therefore, the inequalities that represent the situation are A) 12x + 18y ≥ 325, C) x + y ≤ 20, D) x ≥ 0, and E) y ≥ 0. The inequality B) 12x + 18y ≤ 325 does not correctly represent the situation because Lly wants to save at least $325, not at most $325.