Math / Algebra

Question7) Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $\$ 135$ . Members pay $\$ 2$ to rent out the basketball courts. Non-members can rent the court also, but they have to pay $\$ 11$ each time. how many times would Tom need to rent the court in ord for it be cheaper to be a member than a non member?

Studdy Solution

STEP 1

What is this asking? How many times does Tom need to rent a basketball court so that a gym membership is cheaper than paying the non-member rate each time? Watch out! Don't forget to include the membership cost when calculating the total cost for members.

STEP 2

1. Set up the cost equations.
2. Find the break-even point.

STEP 3

Alright, let's define the total cost for a member and a non-member.
Let $x$ be the number of times Tom rents the court.

STEP 4

The total cost for a member is the $\$135$ membership fee plus $\$2$ per court rental, so the equation is $C_m(x) = 135 + 2 \cdot x$ .

STEP 5

The total cost for a non-member is simply $\$11$ per court rental, so the equation is $C_{nm}(x) = 11 \cdot x$ .

STEP 6

We want to find the number of rentals, $x$ , where the cost of being a member equals the cost of being a non-member.
This is called the break-even point.
So, we set the two equations equal to each other: $135 + 2 \cdot x = 11 \cdot x$ .

STEP 7

Now, let's isolate $x$ .
We can start by subtracting $2 \cdot x$ from both sides of the equation: $135 + 2 \cdot x - 2 \cdot x = 11 \cdot x - 2 \cdot x$ .
This simplifies to $135 = 9 \cdot x$ .

STEP 8

To solve for $x$ , we divide both sides of the equation by $9$ : $\frac{135}{9} = \frac{9 \cdot x}{9}$ .
This gives us $x = 15$ .

STEP 9

Tom would need to rent the court 15 times for the cost of being a member to be the same as the cost of being a non-member.
Therefore, if he rents the court more than 15 times, it's cheaper to be a member!

Was this helpful?

Studdy Solution

STEP 1

What is this asking? How many times does Tom need to rent a basketball court so that a gym membership is cheaper than paying the non-member rate each time? Watch out! Don't forget to include the membership cost when calculating the total cost for members.

STEP 2

1. Set up the cost equations.
2. Find the break-even point.

STEP 3

Alright, let's define the total cost for a member and a non-member.
Let $x$ be the number of times Tom rents the court.

STEP 4

The total cost for a member is the $\$135$ membership fee plus $\$2$ per court rental, so the equation is $C_m(x) = 135 + 2 \cdot x$ .

STEP 5

The total cost for a non-member is simply $\$11$ per court rental, so the equation is $C_{nm}(x) = 11 \cdot x$ .

STEP 6

We want to find the number of rentals, $x$ , where the cost of being a member equals the cost of being a non-member.
This is called the break-even point.
So, we set the two equations equal to each other: $135 + 2 \cdot x = 11 \cdot x$ .

STEP 7

Now, let's isolate $x$ .
We can start by subtracting $2 \cdot x$ from both sides of the equation: $135 + 2 \cdot x - 2 \cdot x = 11 \cdot x - 2 \cdot x$ .
This simplifies to $135 = 9 \cdot x$ .

STEP 8

To solve for $x$ , we divide both sides of the equation by $9$ : $\frac{135}{9} = \frac{9 \cdot x}{9}$ .
This gives us $x = 15$ .

STEP 9

Tom would need to rent the court 15 times for the cost of being a member to be the same as the cost of being a non-member.
Therefore, if he rents the court more than 15 times, it's cheaper to be a member!

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.

Studdy Solution

STEP 1

What is this asking? How many times does Tom need to rent a basketball court so that a gym membership is cheaper than paying the non-member rate each time? Watch out! Don't forget to include the membership cost when calculating the total cost for members.

STEP 2

1. Set up the cost equations.2. Find the break-even point.

STEP 3

Alright, let's **define** the **total cost** for a member and a non-member.Let xxx be the **number of times** Tom rents the court.

STEP 4

The **total cost** for a *member* is the $135\$135$135 **membership fee** plus $2\$2$2 per court rental, so the equation is Cm(x)=135+2⋅xC_m(x) = 135 + 2 \cdot xCm​(x)=135+2⋅x.

STEP 5

The **total cost** for a *non-member* is simply $11\$11$11 per court rental, so the equation is Cnm(x)=11⋅xC_{nm}(x) = 11 \cdot xCnm​(x)=11⋅x.

STEP 6

We want to find the **number of rentals**, xxx, where the **cost of being a member** *equals* the **cost of being a non-member**.This is called the **break-even point**.So, we set the two equations equal to each other: 135+2⋅x=11⋅x135 + 2 \cdot x = 11 \cdot x135+2⋅x=11⋅x.

STEP 7

Now, let's **isolate** xxx.We can start by **subtracting** 2⋅x2 \cdot x2⋅x from both sides of the equation: 135+2⋅x−2⋅x=11⋅x−2⋅x135 + 2 \cdot x - 2 \cdot x = 11 \cdot x - 2 \cdot x135+2⋅x−2⋅x=11⋅x−2⋅x.This simplifies to 135=9⋅x135 = 9 \cdot x135=9⋅x.

STEP 8

To **solve for** xxx, we **divide** both sides of the equation by 999: 1359=9⋅x9\frac{135}{9} = \frac{9 \cdot x}{9}9135​=99⋅x​.This gives us x=15x = 15x=15.

STEP 9

Tom would need to rent the court **15 times** for the cost of being a member to be the same as the cost of being a non-member.Therefore, if he rents the court *more* than 15 times, it's cheaper to be a member!

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.

1. Set up the cost equations.
2. Find the break-even point.

Alright, let's define the total cost for a member and a non-member.
Let $x$ be the number of times Tom rents the court.

The total cost for a member is the $\$135$ membership fee plus $\$2$ per court rental, so the equation is $C_m(x) = 135 + 2 \cdot x$ .

The total cost for a non-member is simply $\$11$ per court rental, so the equation is $C_{nm}(x) = 11 \cdot x$ .

We want to find the number of rentals, $x$ , where the cost of being a member equals the cost of being a non-member.
This is called the break-even point.
So, we set the two equations equal to each other: $135 + 2 \cdot x = 11 \cdot x$ .

Now, let's isolate $x$ .
We can start by subtracting $2 \cdot x$ from both sides of the equation: $135 + 2 \cdot x - 2 \cdot x = 11 \cdot x - 2 \cdot x$ .
This simplifies to $135 = 9 \cdot x$ .

To solve for $x$ , we divide both sides of the equation by $9$ : $\frac{135}{9} = \frac{9 \cdot x}{9}$ .
This gives us $x = 15$ .

Tom would need to rent the court 15 times for the cost of being a member to be the same as the cost of being a non-member.
Therefore, if he rents the court more than 15 times, it's cheaper to be a member!