Question

you are choosing between two different cell - phone plans. the first plan charges a rate of 21 cents per minute. the second plan charges a monthly fee of $29.95 plus 10 cents per minute. let t be the number of minutes you talk and $c_1$ and $c_2$ be the costs (in dollars) of the first and second plans. give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans (round your answer to one decimal place).
$c_1=
$c_2=
if you talk for
minutes the two plans will have the same cost.
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question 10
an executive in an engineering firm earns a monthly salary plus a christmas bonus of 5500 dollars. if she earns a total of 88800 dollars per year, what is her monthly salary in dollars?
your answer is : $
give your answer to the nearest cent.
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Explanation:

Step1: Find the cost - equation for the first plan

The first plan charges 21 cents or $0.21$ per minute. So the cost $C_1$ in terms of the number of minutes $t$ is $C_1 = 0.21t$.

Step2: Find the cost - equation for the second plan

The second plan has a monthly fee of $\$29.95$ and a charge of 10 cents or $0.10$ per minute. So the cost $C_2$ in terms of the number of minutes $t$ is $C_2=29.95 + 0.10t$.

Step3: Set $C_1$ equal to $C_2$ and solve for $t$

Set $0.21t=29.95 + 0.10t$.
Subtract $0.10t$ from both sides:
$0.21t-0.10t=29.95+0.10t - 0.10t$.
$0.11t = 29.95$.
Divide both sides by $0.11$: $t=\frac{29.95}{0.11}\approx272.3$.

Step1: Let the monthly salary be $x$

The executive's annual income consists of 12 months of salary and a Christmas bonus of $5500$. The total annual income is $88800$. So the equation is $12x+5500 = 88800$.

Step2: Solve the equation for $x$

Subtract 5500 from both sides of the equation:
$12x+5500 - 5500=88800 - 5500$.
$12x=83300$.
Divide both sides by 12: $x=\frac{83300}{12}\approx6941.67$.

Answer:

$C_1 = 0.21t$
$C_2=29.95 + 0.10t$
If you talk for $272.3$ minutes the two plans will have the same cost.

For the second - part of the question: