The Fun Guys game rental store charges an annual fee of $20 plus $6.50 per game rented. The Game Bank charges an annual fee of $50 plus $3.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost?
10 games; $85
To find the number of game rentals at which the cost is the same at both stores, we need to set up an equation.
Let's represent the number of game rentals as x.
For Fun Guys: Cost = $20 + $6.50 * x
For Game Bank: Cost = $50 + $3.50 * x
Setting the two costs equal to each other, we get the equation:
$20 + $6.50 * x = $50 + $3.50 * x
To solve for x, we can subtract $20 on both sides and subtract $3.50 * x on both sides:
$6.50 * x - $3.50 * x = $50 - $20
Combining like terms, we have:
$3.00 * x = $30
To isolate x, we divide both sides by $3.00:
x = $30 / $3.00
Simplifying, we have:
x = 10
Therefore, the cost will be the same at both stores when you rent 10 games.
To find that cost, we can substitute x = 10 into either store's cost equation. Let's use Fun Guys:
Cost = $20 + $6.50 * x
Cost = $20 + $6.50 * 10
Cost = $20 + $65
Cost = $85
So, the cost will be $85 when you rent 10 games at either store.
To find the number of game rentals where the cost is the same at both stores, we can set up an equation.
Let's assume the number of game rentals as 'x'.
The cost at Fun Guys game rental store can be expressed as: $20 + $6.50 * x
The cost at Game Bank can be expressed as: $50 + $3.50 * x
Setting the two equations equal, we have:
$20 + $6.50 * x = $50 + $3.50 * x
Now, let's solve this equation to find the value of 'x'.
Subtracting $3.50 * x from both sides:
$20 + $6.50 * x - $3.50 * x = $50 + $3.50 * x - $3.50 * x
Simplifying:
$20 + $3.00 * x = $50
Subtracting $20 from both sides:
$20 + $3.00 * x - $20 = $50 - $20
Simplifying:
$3.00 * x = $30
Dividing both sides by $3.00:
($3.00 * x) / $3.00 = $30 / $3.00
Simplifying:
x = 10
So, the cost will be the same at both stores for 10 game rentals.
Now, let's calculate the cost at that point.
Cost at Fun Guys game rental store = $20 + $6.50 * x
Cost at Fun Guys game rental store = $20 + $6.50 * 10
Cost at Fun Guys game rental store = $20 + $65
Cost at Fun Guys game rental store = $85
Cost at Game Bank = $50 + $3.50 * x
Cost at Game Bank = $50 + $3.50 * 10
Cost at Game Bank = $50 + $35
Cost at Game Bank = $85
Therefore, the cost will be $85 for 10 game rentals at both stores.
20+6.50x = 50+3.50x
Now just find x, and then plug into either side.