The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after
26
minutes of calls is
$16.36
, and the remaining credit after
45
minutes of calls is
$13.70
. What is the remaining credit after
58
minutes of calls?
Well, if the remaining credit after 26 minutes of calls is $16.36 and the remaining credit after 45 minutes of calls is $13.70, then we can determine the linear equation for this situation.
Let's use the point-slope form, where y is the remaining credit and x is the calling time:
(y - y1) = m(x - x1)
Using the two points (26, 16.36) and (45, 13.70), we can find the slope (m):
(m) = (13.70 - 16.36) / (45 - 26)
(m) = -2.66 / 19
(m) ≈ -0.14
Now, let's put this into the equation:
(y - 16.36) = -0.14(x - 26)
Simplifying this equation, we get:
y = -0.14x + 19.44
So, if we plug in x = 58 into this equation, we can find the remaining credit:
y = -0.14(58) + 19.44
y ≈ $11.52
Therefore, the remaining credit after 58 minutes of calls would be approximately $11.52. But hey, don't worry, at least you'll still have some credit for a quick joke! What do you call a phone that can sing? A touch-tone deaf!
To find the remaining credit after 58 minutes of calls, we need to determine the linear function that relates the credit remaining (in dollars) to the total calling time (in minutes).
Let's assign variables:
x = total calling time (in minutes)
y = remaining credit (in dollars)
We are given two data points:
When x = 26, y = $16.36
When x = 45, y = $13.70
Using the two data points, we can set up a system of equations to find the linear function.
From the first data point:
26x + b = 16.36 ........(1)
From the second data point:
45x + b = 13.70 ........(2)
We can solve this system of equations to find the values of x and b by subtracting equation (2) from equation (1):
(26x + b) - (45x + b) = 16.36 - 13.70
26x - 45x = 2.66
Simplifying further:
-19x = 2.66
Dividing both sides by -19:
x = -2.66 / 19
x ≈ -0.14
Now that we have the value of x, we can substitute it back into any of the original equations to find the value of b. Let's use equation (1):
26(-0.14) + b = 16.36
-3.64 + b = 16.36
b = 16.36 + 3.64
b = 20
Now we have the values of x and b for the linear function. The equation is:
y = -0.14x + 20
To find the remaining credit after 58 minutes of calls (x = 58), substitute x = 58 into the equation:
y = -0.14(58) + 20
y = -8.12 + 20
y ≈ $11.88
Therefore, the remaining credit after 58 minutes of calls is approximately $11.88.
To solve this problem, we need to find the equation of the linear function that relates the remaining credit to the total calling time. Let's assume that the remaining credit after x minutes of calls is represented by the variable y.
We are given two data points that we can use to form two equations. From the first data point, when the total calling time is 26 minutes, the remaining credit is $16.36. This can be represented as the equation:
y = mx + b
Substituting the values in, we get:
16.36 = m(26) + b
From the second data point, when the total calling time is 45 minutes, the remaining credit is $13.70. This can be represented as the equation:
13.70 = m(45) + b
Now we have a system of two equations with two unknowns (m and b). We can solve this system of equations to find the values of m and b.
Step 1: Solve the first equation for b in terms of m:
16.36 = 26m + b
b = 16.36 - 26m
Step 2: Replace b in the second equation with the expression we found in step 1:
13.70 = 45m + (16.36 - 26m)
Simplifying the equation:
13.70 = 45m + 16.36 - 26m
Combine like terms:
13.70 = 19m + 16.36
Subtract 16.36 from both sides:
13.70 - 16.36 = 19m + 16.36 - 16.36
Simplify:
-2.66 = 19m
Divide both sides by 19 to solve for m:
m = -2.66 / 19
m ≈ -0.14
Step 3: Substitute the value of m back into either of the original equations to find b. Let's use the first equation:
16.36 = (-0.14)(26) + b
Simplifying the equation:
16.36 = -3.64 + b
Add 3.64 to both sides:
16.36 + 3.64 = -3.64 + b + 3.64
Simplify:
20 = b
So, we have found that m ≈ -0.14 and b = 20. Now we can write the equation for the remaining credit as:
y = -0.14x + 20
To find the remaining credit after 58 minutes of calls, we substitute x = 58 into the equation:
y = -0.14(58) + 20
Calculating the expression:
y ≈ -8.12 + 20
Simplifying:
y ≈ 11.88
Therefore, the remaining credit after 58 minutes of calls is approximately $11.88.