Question

dan is trying to find a new cell phone plan. throttle talks offers a plan for $64.24 a month, plus $2.01 for each megabyte of data. clutch cells offers a plan for $63.74 a month, plus $2.06 for each megabyte of data. how many megabytes of data will dan have to use in one month for the cell phone plans to cost him the same amount?
a. 7.94
b. 10
c. the cost will never be the same.
d. 5

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of megabytes of data. The cost function for Clutch Cells is $C_1 = 63.74+2.06x$. The cost function for Throttle Talks is $C_2=64.24 + 2.01x$.

Step2: Set the two cost - functions equal

We want to find when $C_1 = C_2$, so $63.74+2.06x=64.24 + 2.01x$.

Step3: Solve for $x$

Subtract $2.01x$ from both sides: $63.74+2.06x-2.01x=64.24 + 2.01x-2.01x$, which simplifies to $63.74 + 0.05x=64.24$. Then subtract $63.74$ from both sides: $0.05x=64.24 - 63.74$. So $0.05x=0.5$. Divide both sides by $0.05$: $x=\frac{0.5}{0.05}=10$.

Answer:

B. 10