Brianna needs to buy 3 new work uniforms, which consist of a hat and shirt. Each shirt is $12.50, and the total for her purchase is $62.25. She writes the following equation to help figure out the cost of each hat.

Question

3(c+12.50)=62.25
She solves the equation to get c=8.25.
How could Brianna correctly solve this problem without using the equation?
Responses
Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, divide the sum by 3.

Multiply 3 by $12.50. Then, subtract the product from $62.25. Finally, divide the difference by 3.

Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, multiply the sum by 3.

Multiply 3 by $12.50. Then, add the product to $62.25. Finally, divide the sum by 3.

Answer 1

To determine the cost of each hat without using an equation, Brianna can follow these steps logically:

1. Calculate the total cost of the shirts: Since each shirt costs $12.50 and she is buying 3 shirts, we multiply: \[ 3 \times 12.50 = 37.50. \]

2. Determine the total cost of the hats: The total amount spent on the uniforms is $62.25. To find out how much was spent on the hats, we subtract the total cost of the shirts from the total cost: \[ 62.25 - 37.50 = 24.75. \]

3. Calculate the cost of each hat: Since there are 3 hats, divide the total cost of the hats by 3: \[ \frac{24.75}{3} = 8.25. \]

Let's analyze the response options given:

1. Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, divide the sum by 3. (Incorrect)

2. Multiply 3 by $12.50. Then, subtract the product from $62.25. Finally, divide the difference by 3. (Correct)

3. Divide $12.50 by 3. Then, subtract the quotient from $62.25. Finally, multiply the sum by 3. (Incorrect)

4. Multiply 3 by $12.50. Then, add the product to $62.25. Finally, divide the sum by 3. (Incorrect)

Therefore, the correct process Brianna could have used is the second option: Multiply 3 by $12.50. Then, subtract the product from $62.25. Finally, divide the difference by 3.