QuestionFind $x$ where the trampoline park cost ( $150 + 20x$ ) equals the skating rink cost ( $175 + 15x$ ).

Studdy Solution

STEP 1

Assumptions1. The trampoline park charges a booking fee of $150 and$ 20 for each person who attends. . The skating rink charges a booking fee of $175 and$ 15 for each person who attends.
3. We want to find the number of people, $x$ , for which the cost at both venues will be the same.

STEP 2

First, let's write down the cost function for each venue. The cost function is the total cost of having the party, which is the sum of the booking fee and the cost per person times the number of people.
For the trampoline park, the cost function is $C_{trampoline}(x) =150 +20x$ For the skating rink, the cost function is $C_{skating}(x) =175 +15x$

STEP 3

We want to find the number of people, $x$ , for which the cost at both venues will be the same. This means we need to set the two cost functions equal to each other and solve for $x$ .
$150 +20x =175 +15x$

STEP 4

To isolate $x$ , we can first subtract $150$ from both sides of the equation.
$20x =175 +15x -150$

STEP 5

implify the right side of the equation.
$20x =25 +15x$

STEP 6

Next, subtract $15x$ from both sides of the equation to isolate $x$ .
$20x -15x =25$

STEP 7

implify the left side of the equation.
$5x =25$

STEP 8

Finally, divide both sides of the equation by $5$ to solve for $x$ .
$x =25 /5$

STEP 9

Calculate the value of $x$ .
$x =25 /5 =5$ So,5 people must attend the party in order for the cost of having the party at the trampoline park and the skating rink to be the same.

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QuestionFind $x$ where the trampoline park cost ( $150 + 20x$ ) equals the skating rink cost ( $175 + 15x$ ).

Studdy Solution

STEP 1

Assumptions1. The trampoline park charges a booking fee of $150 and$ 20 for each person who attends. . The skating rink charges a booking fee of $175 and$ 15 for each person who attends.
3. We want to find the number of people, $x$ , for which the cost at both venues will be the same.

STEP 2

STEP 3

We want to find the number of people, $x$ , for which the cost at both venues will be the same. This means we need to set the two cost functions equal to each other and solve for $x$ .
$150 +20x =175 +15x$

STEP 4

To isolate $x$ , we can first subtract $150$ from both sides of the equation.
$20x =175 +15x -150$

STEP 5

implify the right side of the equation.
$20x =25 +15x$

STEP 6

Next, subtract $15x$ from both sides of the equation to isolate $x$ .
$20x -15x =25$

STEP 7

implify the left side of the equation.
$5x =25$

STEP 8

Finally, divide both sides of the equation by $5$ to solve for $x$ .
$x =25 /5$

STEP 9

Calculate the value of $x$ .
$x =25 /5 =5$ So,5 people must attend the party in order for the cost of having the party at the trampoline park and the skating rink to be the same.

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QuestionFind xxx where the trampoline park cost (150+20x150 + 20x150+20x) equals the skating rink cost (175+15x175 + 15x175+15x).

Studdy Solution

STEP 1

STEP 2

STEP 3

We want to find the number of people, xxx, for which the cost at both venues will be the same. This means we need to set the two cost functions equal to each other and solve for xxx.150+20x=175+15x150 +20x =175 +15x150+20x=175+15x

STEP 4

To isolate xxx, we can first subtract 150150150 from both sides of the equation.20x=175+15x−15020x =175 +15x -15020x=175+15x−150

STEP 5

implify the right side of the equation.20x=25+15x20x =25 +15x20x=25+15x

STEP 6

Next, subtract 15x15x15x from both sides of the equation to isolate xxx.20x−15x=2520x -15x =2520x−15x=25

STEP 7

implify the left side of the equation.5x=255x =255x=25

STEP 8

Finally, divide both sides of the equation by 555 to solve for xxx.x=25/5x =25 /5x=25/5

STEP 9

Calculate the value of xxx.x=25/5=5x =25 /5 =5x=25/5=5So,5 people must attend the party in order for the cost of having the party at the trampoline park and the skating rink to be the same.

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

QuestionFind $x$ where the trampoline park cost ( $150 + 20x$ ) equals the skating rink cost ( $175 + 15x$ ).

We want to find the number of people, $x$ , for which the cost at both venues will be the same. This means we need to set the two cost functions equal to each other and solve for $x$ .
$150 +20x =175 +15x$

To isolate $x$ , we can first subtract $150$ from both sides of the equation.
$20x =175 +15x -150$

implify the right side of the equation.
$20x =25 +15x$

Next, subtract $15x$ from both sides of the equation to isolate $x$ .
$20x -15x =25$

implify the left side of the equation.
$5x =25$

Finally, divide both sides of the equation by $5$ to solve for $x$ .
$x =25 /5$

Calculate the value of $x$ .
$x =25 /5 =5$ So,5 people must attend the party in order for the cost of having the party at the trampoline park and the skating rink to be the same.