QuestionFind the number of days when the cost of renting a truck from Company A ( $40d$ ) equals Company B ( $60 + 40d$ ). Show your work.

Studdy Solution

STEP 1

Assumptions1. Company A charges a rate of $40 per day. Company B charges a$ 60 fee plus $40 per day3. We are looking for the number of days where the cost is the same for both companies

STEP 2

First, we need to set up the equations for the cost of renting a truck from each company.For Company A, the cost is $40 per day, so the equation is$ $Cost_{A} =40d$ $where$ d$ is the number of days.

STEP 3

For Company B, the cost is a $60 fee plus$ 40 per day, so the equation is $Cost_{B} =60 +40d$

STEP 4

We want to find the number of days where the cost is the same for both companies, so we can set the two equations equal to each other and solve for $d$ .
$40d =60 +40d$

STEP 5

We can see that the term $40d$ appears on both sides of the equation, so we can subtract $40d$ from both sides to simplify the equation.
$40d -40d =60 +40d -40d$

STEP 6

implify the equation.
$0 =60$

STEP 7

We have reached a contradiction. This means that there are no days where the cost of renting a truck from Company A is the same as the cost of renting a truck from Company B.

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QuestionFind the number of days when the cost of renting a truck from Company A ( $40d$ ) equals Company B ( $60 + 40d$ ). Show your work.

Studdy Solution

STEP 1

Assumptions1. Company A charges a rate of $40 per day. Company B charges a$ 60 fee plus $40 per day3. We are looking for the number of days where the cost is the same for both companies

STEP 2

First, we need to set up the equations for the cost of renting a truck from each company.For Company A, the cost is $40 per day, so the equation is$ $Cost_{A} =40d$ $where$ d$ is the number of days.

STEP 3

For Company B, the cost is a $60 fee plus$ 40 per day, so the equation is $Cost_{B} =60 +40d$

STEP 4

We want to find the number of days where the cost is the same for both companies, so we can set the two equations equal to each other and solve for $d$ .
$40d =60 +40d$

STEP 5

We can see that the term $40d$ appears on both sides of the equation, so we can subtract $40d$ from both sides to simplify the equation.
$40d -40d =60 +40d -40d$

STEP 6

implify the equation.
$0 =60$

STEP 7

We have reached a contradiction. This means that there are no days where the cost of renting a truck from Company A is the same as the cost of renting a truck from Company B.

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QuestionFind the number of days when the cost of renting a truck from Company A (40d40d40d) equals Company B (60+40d60 + 40d60+40d). Show your work.

Studdy Solution

STEP 1

Assumptions1. Company A charges a rate of 40perday.CompanyBchargesa40 per day. Company B charges a 40perday.CompanyBchargesa60 fee plus $40 per day3. We are looking for the number of days where the cost is the same for both companies

STEP 2

First, we need to set up the equations for the cost of renting a truck from each company.For Company A, the cost is 40perday,sotheequationis40 per day, so the equation is40perday,sotheequationisCostA=40dCost_{A} =40dCostA​=40dwherewhere whered$ is the number of days.

STEP 3

For Company B, the cost is a 60feeplus60 fee plus 60feeplus40 per day, so the equation isCostB=60+40dCost_{B} =60 +40dCostB​=60+40d

STEP 4

We want to find the number of days where the cost is the same for both companies, so we can set the two equations equal to each other and solve for ddd.40d=60+40d40d =60 +40d40d=60+40d

STEP 5

We can see that the term 40d40d40d appears on both sides of the equation, so we can subtract 40d40d40d from both sides to simplify the equation.40d−40d=60+40d−40d40d -40d =60 +40d -40d40d−40d=60+40d−40d

STEP 6

implify the equation.0=600 =600=60

STEP 7

We have reached a contradiction. This means that there are no days where the cost of renting a truck from Company A is the same as the cost of renting a truck from Company B.

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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.

QuestionFind the number of days when the cost of renting a truck from Company A ( $40d$ ) equals Company B ( $60 + 40d$ ). Show your work.

Assumptions1. Company A charges a rate of $40 per day. Company B charges a$ 60 fee plus $40 per day3. We are looking for the number of days where the cost is the same for both companies

First, we need to set up the equations for the cost of renting a truck from each company.For Company A, the cost is $40 per day, so the equation is$ $Cost_{A} =40d$ $where$ d$ is the number of days.

For Company B, the cost is a $60 fee plus$ 40 per day, so the equation is $Cost_{B} =60 +40d$

We want to find the number of days where the cost is the same for both companies, so we can set the two equations equal to each other and solve for $d$ .
$40d =60 +40d$

We can see that the term $40d$ appears on both sides of the equation, so we can subtract $40d$ from both sides to simplify the equation.
$40d -40d =60 +40d -40d$

implify the equation.
$0 =60$