Question Marcos' cell phone balance $B=25-0.1n$ where $n$ is minutes talked. a) Initial balance: $\$ 25$ . b) Minutes until balance is $0$ : 250 minutes. c) Slope: $-0.1$ minutes/ $\$$

Studdy Solution

STEP 1

Assumptions
1. The equation modeling Marcos' remaining balance is $B = 25 - 0.1n$ .
2. The variable $B$ represents the remaining balance in dollars.
3. The variable $n$ represents the number of minutes talked since purchasing the card.
4. The equation is linear, with a slope and intercepts that can be identified.

STEP 2

To find the amount of money on the card when Marcos purchased it, we need to determine the initial balance before any minutes were used. This can be found by evaluating the equation when $n = 0$ .

STEP 3

Plug in $n = 0$ into the equation to find the initial balance.
$B = 25 - 0.1(0)$

STEP 4

Calculate the initial balance.
$B = 25 - 0 = 25$
The initial balance on the card when Marcos purchased it was $25.

STEP 5

Identify which intercept the initial balance represents. Since we found the balance when $n = 0$ , this is the B-intercept, also known as the y-intercept in the context of a graph.

STEP 6

To find out how many minutes Marcos will have talked when he runs out of money, we need to determine the value of $n$ when the remaining balance $B$ is zero.

STEP 7

Set the remaining balance $B$ to zero and solve for $n$ .
$0 = 25 - 0.1n$

STEP 8

Add $0.1n$ to both sides of the equation to isolate $n$ on one side.
$0.1n = 25$

STEP 9

Divide both sides of the equation by $0.1$ to solve for $n$ .
$n = \frac{25}{0.1}$

STEP 10

Calculate the value of $n$ .
$n = \frac{25}{0.1} = 250$
Marcos will have talked for 250 minutes when he runs out of money.

STEP 11

Identify which intercept the number of minutes represents. Since we found the number of minutes when $B = 0$ , this is the n-intercept, also known as the x-intercept in the context of a graph.

STEP 12

To determine the slope of the equation, we look at the coefficient of $n$ in the equation $B = 25 - 0.1n$ .

STEP 13

The slope is the coefficient of $n$ , which is $-0.1$ .

STEP 14

Identify the units on the slope. Since the slope represents the rate of change of the balance with respect to the number of minutes talked, the units are dollars per minute.
The slope of the equation is $-0.1$ dollars per minute.

Was this helpful?

Question Marcos' cell phone balance $B=25-0.1n$ where $n$ is minutes talked. a) Initial balance: $\$ 25$ . b) Minutes until balance is $0$ : 250 minutes. c) Slope: $-0.1$ minutes/ $\$$

Studdy Solution

STEP 1

STEP 2

To find the amount of money on the card when Marcos purchased it, we need to determine the initial balance before any minutes were used. This can be found by evaluating the equation when $n = 0$ .

STEP 3

Plug in $n = 0$ into the equation to find the initial balance.
$B = 25 - 0.1(0)$

STEP 4

Calculate the initial balance.
$B = 25 - 0 = 25$
The initial balance on the card when Marcos purchased it was $25.

STEP 5

Identify which intercept the initial balance represents. Since we found the balance when $n = 0$ , this is the B-intercept, also known as the y-intercept in the context of a graph.

STEP 6

To find out how many minutes Marcos will have talked when he runs out of money, we need to determine the value of $n$ when the remaining balance $B$ is zero.

STEP 7

Set the remaining balance $B$ to zero and solve for $n$ .
$0 = 25 - 0.1n$

STEP 8

Add $0.1n$ to both sides of the equation to isolate $n$ on one side.
$0.1n = 25$

STEP 9

Divide both sides of the equation by $0.1$ to solve for $n$ .
$n = \frac{25}{0.1}$

STEP 10

Calculate the value of $n$ .
$n = \frac{25}{0.1} = 250$
Marcos will have talked for 250 minutes when he runs out of money.

STEP 11

Identify which intercept the number of minutes represents. Since we found the number of minutes when $B = 0$ , this is the n-intercept, also known as the x-intercept in the context of a graph.

STEP 12

To determine the slope of the equation, we look at the coefficient of $n$ in the equation $B = 25 - 0.1n$ .

STEP 13

The slope is the coefficient of $n$ , which is $-0.1$ .

STEP 14

Identify the units on the slope. Since the slope represents the rate of change of the balance with respect to the number of minutes talked, the units are dollars per minute.
The slope of the equation is $-0.1$ dollars per minute.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Marcos' cell phone balance B=25−0.1nB=25-0.1nB=25−0.1n where nnn is minutes talked. a) Initial balance: $25\$ 25$25. b) Minutes until balance is 000: 250 minutes. c) Slope: −0.1-0.1−0.1 minutes/$\$$

Studdy Solution

STEP 1

STEP 2

To find the amount of money on the card when Marcos purchased it, we need to determine the initial balance before any minutes were used. This can be found by evaluating the equation when n=0 n = 0 n=0.

STEP 3

Plug in n=0 n = 0 n=0 into the equation to find the initial balance.B=25−0.1(0) B = 25 - 0.1(0) B=25−0.1(0)

STEP 4

Calculate the initial balance.B=25−0=25 B = 25 - 0 = 25 B=25−0=25The initial balance on the card when Marcos purchased it was $25.

STEP 5

Identify which intercept the initial balance represents. Since we found the balance when n=0 n = 0 n=0, this is the B-intercept, also known as the y-intercept in the context of a graph.

STEP 6

To find out how many minutes Marcos will have talked when he runs out of money, we need to determine the value of n n n when the remaining balance B B B is zero.

STEP 7

Set the remaining balance B B B to zero and solve for n n n.0=25−0.1n 0 = 25 - 0.1n 0=25−0.1n

STEP 8

Add 0.1n 0.1n 0.1n to both sides of the equation to isolate n n n on one side.0.1n=25 0.1n = 25 0.1n=25

STEP 9

Divide both sides of the equation by 0.1 0.1 0.1 to solve for n n n.n=250.1 n = \frac{25}{0.1} n=0.125​

STEP 10

Calculate the value of n n n.n=250.1=250 n = \frac{25}{0.1} = 250 n=0.125​=250Marcos will have talked for 250 minutes when he runs out of money.

STEP 11

Identify which intercept the number of minutes represents. Since we found the number of minutes when B=0 B = 0 B=0, this is the n-intercept, also known as the x-intercept in the context of a graph.

STEP 12

To determine the slope of the equation, we look at the coefficient of n n n in the equation B=25−0.1n B = 25 - 0.1n B=25−0.1n.

STEP 13

The slope is the coefficient of n n n, which is −0.1 -0.1 −0.1.

STEP 14

Identify the units on the slope. Since the slope represents the rate of change of the balance with respect to the number of minutes talked, the units are dollars per minute.The slope of the equation is −0.1 -0.1 −0.1 dollars per minute.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Marcos' cell phone balance $B=25-0.1n$ where $n$ is minutes talked. a) Initial balance: $\$ 25$ . b) Minutes until balance is $0$ : 250 minutes. c) Slope: $-0.1$ minutes/ $\$$

To find the amount of money on the card when Marcos purchased it, we need to determine the initial balance before any minutes were used. This can be found by evaluating the equation when $n = 0$ .

Plug in $n = 0$ into the equation to find the initial balance.
$B = 25 - 0.1(0)$

Calculate the initial balance.
$B = 25 - 0 = 25$
The initial balance on the card when Marcos purchased it was $25.

Identify which intercept the initial balance represents. Since we found the balance when $n = 0$ , this is the B-intercept, also known as the y-intercept in the context of a graph.

To find out how many minutes Marcos will have talked when he runs out of money, we need to determine the value of $n$ when the remaining balance $B$ is zero.

Set the remaining balance $B$ to zero and solve for $n$ .
$0 = 25 - 0.1n$

Add $0.1n$ to both sides of the equation to isolate $n$ on one side.
$0.1n = 25$

Divide both sides of the equation by $0.1$ to solve for $n$ .
$n = \frac{25}{0.1}$

Calculate the value of $n$ .
$n = \frac{25}{0.1} = 250$
Marcos will have talked for 250 minutes when he runs out of money.

Identify which intercept the number of minutes represents. Since we found the number of minutes when $B = 0$ , this is the n-intercept, also known as the x-intercept in the context of a graph.

To determine the slope of the equation, we look at the coefficient of $n$ in the equation $B = 25 - 0.1n$ .

The slope is the coefficient of $n$ , which is $-0.1$ .

Identify the units on the slope. Since the slope represents the rate of change of the balance with respect to the number of minutes talked, the units are dollars per minute.
The slope of the equation is $-0.1$ dollars per minute.