The center is consideirng signing up for an online game-rental service rather than buying the games. The table shows equipment cost and monthly fees for two services.

Equipment cost mouthy cost

Net games 99$ 8$

Equipment cost mouthy fee

anytime games 19$ 19$


1. Write and solve an inequality that represents the number of months the center could rent games from NetGames with its $175. Explain the solution in terms of the problem.


2. Write and solve an inequality to represent the number of months the center could rent games from Anytime Games. Explain the solution in terms of the problem.


3. Use your answers from 1 and 2 to justify which service the community center should purchase.

Answer:

Here's what I get  

Step-by-step explanation:

Total cost = equipment cost + monthly fee × number of months

Let C = total cost

and e = equipment cost

and f = monthly fee

and x = number of months. Then

C = e + f·x  

The condition is that C ≤ $175 or

e + f·x ≤ $175

1. NetGear

e = $99; f = $5/mo

The condition is  

99 + 5x ≤ 175

[tex]\begin{array}{rcll}99 + 5x & \leq & 175 &\\5x & \leq &76 & \text{Subtracted 99 from each side}\\x & \leq & \dfrac{76}{5} & \text{Divided each side by 5}\\\\x & \leq & \mathbf{15.2} & \text{Simplified}\\\end{array}\\[/tex]

The centre could rent the games for 15 mo.

They would pay $99 for the equipment.

Fifteen months rental at $5/mo = $75.

Total cost = $174.

2. Anytime Games

e = $19; f = $19/mo

The condition is  

19 + 19x ≤ 175

[tex]\begin{array}{rcll}19 + 19x & \leq & 175&\\19x& \leq & 156 & \text{Subtracted 19 from each side}\\x & \leq & \dfrac{156}{19} & \text{Divided each side by 19}\\\\x & \leq & \mathbf{8.2} & \text{Simplified}\\\end{array}\\[/tex]

The centre could rent the games for eight months.

They would pay $19 for the equipment.

Eight months rental at $19/mo = $152.

Total cost = $171.

3. Recommendation

The Community Centre should rent from NetGear.

They can rent for 15 mo without going over the budget.

With the other company, they can rent for only eight months.

The graphs below show how the costs for the two companies vary with the number of months.

Anything above the horizontal orange line at C = $175 is beyond the Community Centre's budget.  

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