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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 40 minutes of calls is $15.60 and the monthly cost for 62 minutes is $18.46. What is the monthly cost for 56 minutes of calls?

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for $40$ minutes of calls is $\$15.60$ and the monthly cost for $62$ minutes is $\$18.46$ . What is the monthly cost for $56$ minutes of calls?

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Evaluate two-variable equations: word problems

Full solution

Q. The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for

40

minutes of calls is

\$15.60

and the monthly cost for

62

minutes is

\$18.46

. What is the monthly cost for

56

minutes of calls?

Identify Known Points: Step $1$ : Identify the known points and the variable to find. $\newline$ We know the cost for $40$ minutes is $\$15.60$ and for $62$ minutes is $\$18.46$ . We need to find the cost for $56$ minutes.
Calculate Slope: Step $2$ : Calculate the slope (rate of change) of the cost function. $\newline$ Slope $m$ = (Change in cost) / (Change in minutes) = $\$\$18.46 - \$15.60$ / ( $62$ - $40$ )\) $\newline$ $m = \$2.86 / 22 = \$0.13$ per minute.
Use Point-Slope Form: Step $3$ : Use the point-slope form of the linear equation to find the equation of the line. $\newline$ Using the point $(40, \$15.60)$ and slope $\$0.13$ : $\newline$ Cost = $\$15.60 + \$0.13 \times (\text{Minutes} - 40)$
Substitute to Find Cost: Step $4$ : Substitute $56$ for the minutes in the equation to find the cost for $56$ minutes. $\newline$ Cost for $56$ minutes = $\$15.60 + \$0.13 \times (56 - 40)$ $\newline$ Cost for $56$ minutes = $\$15.60 + \$0.13 \times 16$ $\newline$ Cost for $56$ minutes = $\$15.60 + \$2.08$ $\newline$ Cost for $56$ minutes = $\$17.68$

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