Patricia wants to buy a new phone, and the cheapest one she likes is $175. Each week, she earns $25 from babysitting and a paycheck from an hourly job.

Question

This inequality represents what Patricia needs to earn, where x represents the number of hours she needs to work to save enough money for the phone.
12.5x+25≥175
Which statement is true about the solution for the inequality that represents this situation?
Responses
Patricia needs to work less than 12 hours to save enough money for the phone.
.
Patricia needs to work at most 12 hours to save enough money for the phone.

Patricia needs to work at least 12 hours to save enough money for the phone.
.
Patricia needs to work more than 12 hours to save enough money for the phone.

Answer 1

To solve the inequality \(12.5x + 25 \geq 175\), we first isolate the term with \(x\):

1. Subtract 25 from both sides: \[ 12.5x \geq 175 - 25 \] \[ 12.5x \geq 150 \]

2. Now, divide both sides by 12.5: \[ x \geq \frac{150}{12.5} \] \[ x \geq 12 \]

So, the solution to the inequality is \(x \geq 12\).

This means that Patricia needs to work at least 12 hours to save enough money for the phone.

Therefore, the true statement from the options given is:

Patricia needs to work at least 12 hours to save enough money for the phone.