QuestionSolve for $x$ : When is the cost of the trampoline park, $150 + 20x$ , equal to the skating rink, $175 + 15x$ ?

Studdy Solution

STEP 1

Assumptions1. The inequality is $4b +3 \leq6b$ . The cost of each binder is represented by $b$
3. The cost of a pack of markers is $34. The cost of four binders and a pack of markers is less than or equal to the cost of six binders

STEP 2

We need to solve the inequality to find the relationship between the cost of four binders and a pack of markers and the cost of six binders. $4b + \leq6b$

STEP 3

Subtract $b$ from both sides of the inequality to isolate the variable $b$ on one side.
$b -b +3 \leq6b -b$

STEP 4

implify the inequality.
$3 \leq2b$

STEP 5

Divide both sides of the inequality by $2$ to solve for $b$ .
$\frac{3}{2} \leq b$ This means that the cost of each binder must be at least $1.5. Therefore, the correct answer is D. Four binders and a$ 3 pack of markers cost no more than six binders.

STEP 6

Assumptions for the second problem1. The trampoline park charges a booking fee of $150 and$ 20 for each person who attends the party.
2. The skating rink charges a booking fee of $175 and$ 15 for each person who attends the party.
3. We need to find the number of people, $x$ , for which the cost of the party at both places will be the same.

STEP 7

Set up an equation to represent the cost of the party at both places. $150 +20x =175 +15x$

STEP 8

Subtract $150$ and $15x$ from both sides of the equation to isolate the variable $x$ on one side.
$20x -15x =175 -150$

STEP 9

implify the equation.
$5x =25$

STEP 10

Divide both sides of the equation by $5$ to solve for $x$ .
$x = \frac{25}{5}$

STEP 11

Calculate the value of $x$ .
$x =5$ Therefore, if5 people attend the party, the cost of having the party at the trampoline park and the skating rink will be the same.

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QuestionSolve for $x$ : When is the cost of the trampoline park, $150 + 20x$ , equal to the skating rink, $175 + 15x$ ?

Studdy Solution

STEP 1

Assumptions1. The inequality is $4b +3 \leq6b$ . The cost of each binder is represented by $b$
3. The cost of a pack of markers is $34. The cost of four binders and a pack of markers is less than or equal to the cost of six binders

STEP 2

We need to solve the inequality to find the relationship between the cost of four binders and a pack of markers and the cost of six binders. $4b + \leq6b$

STEP 3

Subtract $b$ from both sides of the inequality to isolate the variable $b$ on one side.
$b -b +3 \leq6b -b$

STEP 4

implify the inequality.
$3 \leq2b$

STEP 5

Divide both sides of the inequality by $2$ to solve for $b$ .
$\frac{3}{2} \leq b$ This means that the cost of each binder must be at least $1.5. Therefore, the correct answer is D. Four binders and a$ 3 pack of markers cost no more than six binders.

STEP 6

STEP 7

Set up an equation to represent the cost of the party at both places. $150 +20x =175 +15x$

STEP 8

Subtract $150$ and $15x$ from both sides of the equation to isolate the variable $x$ on one side.
$20x -15x =175 -150$

STEP 9

implify the equation.
$5x =25$

STEP 10

Divide both sides of the equation by $5$ to solve for $x$ .
$x = \frac{25}{5}$

STEP 11

Calculate the value of $x$ .
$x =5$ Therefore, if5 people attend the party, the cost of having the party at the trampoline park and the skating rink will be the same.

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QuestionSolve for xxx: When is the cost of the trampoline park, 150+20x150 + 20x150+20x, equal to the skating rink, 175+15x175 + 15x175+15x?

Studdy Solution

STEP 1

Assumptions1. The inequality is 4b+3≤6b4b +3 \leq6b4b+3≤6b . The cost of each binder is represented by bbb3. The cost of a pack of markers is $34. The cost of four binders and a pack of markers is less than or equal to the cost of six binders

STEP 2

We need to solve the inequality to find the relationship between the cost of four binders and a pack of markers and the cost of six binders.4b+≤6b4b + \leq6b4b+≤6b

STEP 3

Subtract bbb from both sides of the inequality to isolate the variable bbb on one side.b−b+3≤6b−bb -b +3 \leq6b -bb−b+3≤6b−b

STEP 4

implify the inequality.3≤2b3 \leq2b3≤2b

STEP 5

STEP 6

STEP 7

Set up an equation to represent the cost of the party at both places.150+20x=175+15x150 +20x =175 +15x150+20x=175+15x

STEP 8

Subtract 150150150 and 15x15x15x from both sides of the equation to isolate the variable xxx on one side.20x−15x=175−15020x -15x =175 -15020x−15x=175−150

STEP 9

implify the equation.5x=255x =255x=25

STEP 10

Divide both sides of the equation by 555 to solve for xxx.x=255x = \frac{25}{5}x=525​

STEP 11

Calculate the value of xxx.x=5x =5x=5Therefore, if5 people attend the party, the cost of having the party at the trampoline park and the skating rink will be the same.

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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.

QuestionSolve for $x$ : When is the cost of the trampoline park, $150 + 20x$ , equal to the skating rink, $175 + 15x$ ?

Assumptions1. The inequality is $4b +3 \leq6b$ . The cost of each binder is represented by $b$
3. The cost of a pack of markers is $34. The cost of four binders and a pack of markers is less than or equal to the cost of six binders

We need to solve the inequality to find the relationship between the cost of four binders and a pack of markers and the cost of six binders. $4b + \leq6b$

Subtract $b$ from both sides of the inequality to isolate the variable $b$ on one side.
$b -b +3 \leq6b -b$

implify the inequality.
$3 \leq2b$

Set up an equation to represent the cost of the party at both places. $150 +20x =175 +15x$

Subtract $150$ and $15x$ from both sides of the equation to isolate the variable $x$ on one side.
$20x -15x =175 -150$

implify the equation.
$5x =25$

Divide both sides of the equation by $5$ to solve for $x$ .
$x = \frac{25}{5}$

Calculate the value of $x$ .
$x =5$ Therefore, if5 people attend the party, the cost of having the party at the trampoline park and the skating rink will be the same.