Question

Brice has twice as many stamps in his collection as his friends Anthony and Paul combined. Paul has 32 stamps in his collection. Brice has 96 stamps in his collection. How many stamps does Anthony have in his collection?

The equation 2(x + 32) = 96 models this situation. Which choice shows the sequence of operations needed to solve this problem, using both arithmetic and algebra?
A) x + 32 = 96, x = 64, Anthony has 64 stamps.
B) 2x + 64 = 96, x = 16, Anthony has 16 stamps.
C) x + 32 = 96, x = 128, Anthony has 128 stamps.
D) 2x + 32 = 96, x = 32, Anthony has 32 stamps.

Answer 1

To find out how many stamps Anthony has, the algebraic equation 2(x + 32) = 96 needs to be solved. Following algebraic procedures to isolate x, we find that Anthony has 16 stamps in his collection, making option B correct.

Step-by-step explanation:

The question requires solving an algebraic equation to determine how many stamps Anthony has in his collection. Given the equation 2(x + 32) = 96, we follow the sequence of operations to solve for x, which represents the number of stamps Anthony has:

1. Divide both sides of the equation by 2 to isolate the terms with x: x + 32 = 48.
2. Subtract 32 from both sides to solve for x: x = 48 - 32.
3. Calculate the value of x: x = 16, which indicates that Anthony has 16 stamps.

Therefore, option B is correct, and it shows the correct sequence of operations to solve the problem.