Math Equation. Precalc

Question

The remaining credit after
45 minutes of calls is  $14.15, and the remaining credit after  77 minutes of calls is $9.99. What is the remaining credit after 101 minutes of calls?

Answer 1

Translation into equations is the hard part of word problems. Since this is a precalculus problem, I will assume you understand the notion of a linear equation
Y = mx + b
First let’s identify the quantities we need
Let y = credit
Let m = credit per minute in dollars
Let x be number of minutes
Let b = original credit (perhaps you bought a calling card, with $b on it. We don’t know what it is right now)
Let r be credit after 101 minutes
Now write equations for the two data points we know and for the unknown r
14.15 = 45m + b
9.99 = 77m + b
R = 101m + b
Solve for m by subtracting the top line from the middle (this gets rid of b for a moment)
-4.16 = 32 m
m = - .13
Notice this is negative. That makes sense, because each minute you talk REDUCES the amount of remaining credit.
Now we can solve for b, which we’ll need for the third equation.
Substitute this value of m into either equation
14.15 = 45m + b
14.15= 45(-.13) + b
14.15= -5.85 + b
b = $20 (ok, now we know you had bought a $20 card)

Now substitute both m and b into third equation to solve for r
R = (-.13)101 + 20
R = 20-13.13 = 6.87