raul has $460 in his checking account. each month, $45 is automatically deducted from his account to pay for…

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?\no 7 months\no 8 months\no 9 months\no 10 months

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?\no 7 months\no 8 months\no 9 months\no 10 months

Answer

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. So $m < \frac{360}{45}$, and $\frac{360}{45}=8$. Since $m$ represents the number of months and must be an integer, the greatest value of $m$ such that the inequality holds is $m = 7$.

Answer:

A. 7 months