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 . The store orders a total of 8,250 cards.
How many of the cards are T-shirt cards? Show your work.

Question

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

. The store orders a total of 8,250 cards.
How many of the cards are T-shirt cards? Show your work.

UpStudy AI · Accepted Answer

To determine how many of the 8,250 scratch-off cards are T-shirt cards, we'll use the given ratio of coupon cards to T-shirt cards, which is $$ 9:2 $$.

### Step 1: Understanding the Ratio
The ratio $$ 9:2 $$ means that for every **9 coupon cards**, there are **2 T-shirt cards**.

### Step 2: Representing the Numbers with a Variable
Let's introduce a variable to represent the common multiplier for the ratio parts.

- Let $$ x $$ be the multiplier.
- Number of **coupon cards** = $$ 9x $$
- Number of **T-shirt cards** = $$ 2x $$

### Step 3: Setting Up the Equation
The total number of cards is the sum of coupon cards and T-shirt cards:
$$
9x + 2x = 11x
$$
According to the problem, this total is **8,250** cards:
$$
11x = 8,250
$$

### Step 4: Solving for $$ x $$
$$
x = \frac{8,250}{11} = 750
$$

### Step 5: Finding the Number of T-shirt Cards
Now, substitute $$ x = 750 $$ back into the expression for T-shirt cards:
$$
\text{Number of T-shirt cards} = 2x = 2 \times 750 = 1,500
$$

### **Answer:**
There are **1,500 T-shirt cards**.
There are 1,500 T-shirt cards.

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 . The store orders a total of 8,250 cards.
How many of the cards are T-shirt cards? Show your work.

Upstudy AI Solution

Answer

Solution

The Deep Dive

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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 . The store orders a total of 8,250 cards. How many of the cards are T-shirt cards? Show your work.

Upstudy AI Solution

Answer

Solution

The Deep Dive

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Latest Arithmetic Questions

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 . The store orders a total of 8,250 cards.
How many of the cards are T-shirt cards? Show your work.