A store gives scratch-off cards to its customers. For each card, a customer wins either a coupon or a free T-shirt. The ratio of coupon cards to T-shirt cards is \( 9: 2 \). The store orders a total of 8,250 cards. How many of the cards are T-shirt cards? Show your work.

To find the number of T-shirt cards, we'll start by using the given ratio of coupon cards to T-shirt cards, which is \( 9: 2 \). This means for every 9 coupon cards, there are 2 T-shirt cards. Let's denote the number of coupon cards as \( 9x \) and the number of T-shirt cards as \( 2x \). According to the problem, the total number of cards is \( 8,250 \). Therefore, we can set up the equation: \[ 9x + 2x = 8,250 \] \[ 11x = 8,250 \] Now, solving for \( x \): \[ x = \frac{8,250}{11} = 750 \] Now, we can substitute \( x \) back into the expressions for the coupon and T-shirt cards: The number of T-shirt cards is: \[ 2x = 2 \times 750 = 1,500 \] Thus, the number of T-shirt cards is \( \boxed{1,500} \).