QuestionFind the number of text messages where the costs of the two plans, $\$ 29.94 + 0.10x$ and $\$ 32.99 + 0.05x$ , are equal.

Studdy Solution

STEP 1

Assumptions1. The cost of the first plan is $29.94 per month plus$ 0.10 for each text message sent. . The cost of the second plan is $32.99 per month plus$ 0.05 for each text message sent.
3. We are looking for the number of text messages for which the monthly bill for both plans will be the same.

STEP 2

Let's denote the number of text messages as $x$ . Then, we can write the cost of each plan as a function of $x$ .
For the first plan $Cost1 =29.94 +0.10x$ For the second plan $Cost2 =32.99 +0.05x$

STEP 3

We are looking for the number of text messages for which the cost of both plans is the same. Therefore, we set the two cost functions equal to each other and solve for $x$ .
$29.94 +0.10x =32.99 +0.05x$

STEP 4

To solve for $x$ , we first subtract $0.05x$ from both sides of the equation to get the $x$ terms on one side and the constants on the other.
$0.10x -0.05x =32.99 -29.94$

STEP 5

implify both sides of the equation.
$0.05x =3.05$

STEP 6

Finally, solve for $x$ by dividing both sides of the equation by $0.05$ .
$x = \frac{3.05}{0.05}$

STEP 7

Calculate the value of $x$ .
$x = \frac{3.05}{0.05} =61$ So, the monthly bill for both plans will be the same when61 text messages are sent.

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QuestionFind the number of text messages where the costs of the two plans, $\$ 29.94 + 0.10x$ and $\$ 32.99 + 0.05x$ , are equal.

Studdy Solution

STEP 1

Assumptions1. The cost of the first plan is $29.94 per month plus$ 0.10 for each text message sent. . The cost of the second plan is $32.99 per month plus$ 0.05 for each text message sent.
3. We are looking for the number of text messages for which the monthly bill for both plans will be the same.

STEP 2

Let's denote the number of text messages as $x$ . Then, we can write the cost of each plan as a function of $x$ .
For the first plan $Cost1 =29.94 +0.10x$ For the second plan $Cost2 =32.99 +0.05x$

STEP 3

We are looking for the number of text messages for which the cost of both plans is the same. Therefore, we set the two cost functions equal to each other and solve for $x$ .
$29.94 +0.10x =32.99 +0.05x$

STEP 4

To solve for $x$ , we first subtract $0.05x$ from both sides of the equation to get the $x$ terms on one side and the constants on the other.
$0.10x -0.05x =32.99 -29.94$

STEP 5

implify both sides of the equation.
$0.05x =3.05$

STEP 6

Finally, solve for $x$ by dividing both sides of the equation by $0.05$ .
$x = \frac{3.05}{0.05}$

STEP 7

Calculate the value of $x$ .
$x = \frac{3.05}{0.05} =61$ So, the monthly bill for both plans will be the same when61 text messages are sent.

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QuestionFind the number of text messages where the costs of the two plans, $29.94+0.10x\$ 29.94 + 0.10x$29.94+0.10x and $32.99+0.05x\$ 32.99 + 0.05x$32.99+0.05x, are equal.

Studdy Solution

STEP 1

STEP 2

Let's denote the number of text messages as xxx. Then, we can write the cost of each plan as a function of xxx.For the first planCost1=29.94+0.10xCost1 =29.94 +0.10xCost1=29.94+0.10xFor the second planCost2=32.99+0.05xCost2 =32.99 +0.05xCost2=32.99+0.05x

STEP 3

We are looking for the number of text messages for which the cost of both plans is the same. Therefore, we set the two cost functions equal to each other and solve for xxx.29.94+0.10x=32.99+0.05x29.94 +0.10x =32.99 +0.05x29.94+0.10x=32.99+0.05x

STEP 4

To solve for xxx, we first subtract 0.05x0.05x0.05x from both sides of the equation to get the xxx terms on one side and the constants on the other.0.10x−0.05x=32.99−29.940.10x -0.05x =32.99 -29.940.10x−0.05x=32.99−29.94

STEP 5

implify both sides of the equation.0.05x=3.050.05x =3.050.05x=3.05

STEP 6

Finally, solve for xxx by dividing both sides of the equation by 0.050.050.05.x=3.050.05x = \frac{3.05}{0.05}x=0.053.05​

STEP 7

Calculate the value of xxx.x=3.050.05=61x = \frac{3.05}{0.05} =61x=0.053.05​=61So, the monthly bill for both plans will be the same when61 text messages are sent.

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

QuestionFind the number of text messages where the costs of the two plans, $\$ 29.94 + 0.10x$ and $\$ 32.99 + 0.05x$ , are equal.

Let's denote the number of text messages as $x$ . Then, we can write the cost of each plan as a function of $x$ .
For the first plan $Cost1 =29.94 +0.10x$ For the second plan $Cost2 =32.99 +0.05x$

We are looking for the number of text messages for which the cost of both plans is the same. Therefore, we set the two cost functions equal to each other and solve for $x$ .
$29.94 +0.10x =32.99 +0.05x$

To solve for $x$ , we first subtract $0.05x$ from both sides of the equation to get the $x$ terms on one side and the constants on the other.
$0.10x -0.05x =32.99 -29.94$

implify both sides of the equation.
$0.05x =3.05$

Finally, solve for $x$ by dividing both sides of the equation by $0.05$ .
$x = \frac{3.05}{0.05}$

Calculate the value of $x$ .
$x = \frac{3.05}{0.05} =61$ So, the monthly bill for both plans will be the same when61 text messages are sent.