Question

1. glenn has $1,250 in his savings account. in order to avoid bank fees, glenn must keep a minimum of $150 in his account. his cell phone costs him $35 per month. use an inequality to determine how many months glenn can pay for his cell phone before he would incur fees.

Explanation:

Step1: Set up the inequality

Let $m$ be the number of months. The initial amount is $1250$, and he spends $35m$ in $m$ months. He must keep at least $150$. So the inequality is $1250 - 35m\geq150$.

Step2: Solve for $m$

First, subtract 1250 from both sides: $- 35m\geq150 - 1250$. So $-35m\geq - 1100$.

Step3: Divide both sides by - 35

When dividing an inequality by a negative number, the inequality sign flips. So $m\leq\frac{1100}{35}=\frac{220}{7}\approx31.43$.
Since $m$ represents the number of months and it must be a non - negative integer, the maximum value of $m$ is 31.

Answer:

$m\leq31$ (where $m$ is the number of months)