Final answer:
To determine when the gold and silver rental cards cost the same, we set up an equation based on their respective costs and solved for the number of rentals required. The equation is 25 + 1.75x = 10 + 3.25x, which simplifies to x = 10, meaning at 10 rentals, the costs are equal.
Step-by-step explanation:
To find the number of rentals for which the cost of the gold and silver rental cards would be the same, we need to set up an equation and solve for the number of rentals.
Let x be the number of movie rentals.
The cost for the gold card is $25 plus $1.75 per rental, so the gold card cost is represented by the equation 25 + 1.75x.
The cost for the silver card is $10 plus $3.25 per rental, so the silver card cost is represented by the equation 10 + 3.25x.
Setting the two equations equal to each other gives us the equation to solve:
25 + 1.75x = 10 + 3.25x
Subtracting 1.75x from both sides, we get:
25 = 10 + 1.5x
Subtracting 10 from both sides, we have:
15 = 1.5x
Dividing both sides by 1.5, we find:
x = 10
So, the number of rentals at which the cost for both the gold and silver cards is the same is 10 rentals.