Question

gabe and his sister lola both got new cell phones. gabe bought his phone for $350, and his plan costs $30 per month. lola bought her phone for $140, but because she added an extended warranty, her plan costs $44 per month. after how many months will gabe and lola have spent the same amount on their cell phones and plans? months

Explanation:

Step1: Set up cost - equations

Let $m$ be the number of months. Gabe's total cost $C_G$ is the sum of the phone cost and the monthly - plan cost for $m$ months, so $C_G = 350+30m$. Lola's total cost $C_L$ is the sum of her phone cost and her monthly - plan cost for $m$ months, so $C_L=140 + 44m$.

Step2: Set the two equations equal

We want to find when $C_G = C_L$, so we set up the equation $350+30m=140 + 44m$.

Step3: Solve for $m$

First, subtract $30m$ from both sides: $350=140 + 44m-30m$, which simplifies to $350=140 + 14m$. Then subtract 140 from both sides: $350 - 140=14m$, so $210 = 14m$. Divide both sides by 14: $m=\frac{210}{14}=15$.

Answer:

15