Question

raul has $460 in his checking account. each month, $45 is automatically deducted from his account to pay for his cell phone plan. he makes no other deposits or withdrawals. he wants to always have more than $100 in his account. what is the greatest number of months he can pay for his cell phone and still have more than $100 in his account?
o 7 months
o 8 months
o 9 months
o 10 months

Explanation:

Step1: Set up an inequality

Let $m$ be the number of months. The initial amount is $460$, and $45$ is deducted each month. We want the remaining amount $460 - 45m>100$.

Step2: Solve the inequality for $m$

First, subtract 460 from both sides: $- 45m>100 - 460$. So, $-45m>-360$. Then divide both sides by - 45. When dividing an inequality by a negative number, the inequality sign flips. We get $m < \frac{360}{45}$.

Step3: Calculate the value of $m$

$\frac{360}{45}=8$. Since $m < 8$, the greatest whole - number value of $m$ is 7.

Answer:

7 months