Question

Did you know that word problems can help you understand and apply mathematical expressions? Let's create a word problem for the expression 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2) and solve it! Imagine you have a bag of marbles. You take half of the marbles out and then subtract half of a marble from what you have. Next, you repeat this process and take half of the remaining marbles out, followed by subtracting half of a marble once again. You continue doing this until all marbles are gone. In the end, you are left with just one marble. Now, the question arises: How many marbles did you initially have in the bag? By setting up the equation 1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2), where x represents the initial number of marbles, we can solve for x and find out the answer. This word problem allows us to dive into the world of mathematics and engage in problem-solving using algebraic expressions. By experimenting and understanding how different mathematical operations affect the quantity, we gain valuable insights into the intricacies of mathematics.

Answer 1

Great word problem! Let's solve it step by step:

Given:
1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2)

Step 1: Simplify the expression inside the first parenthesis.
1 = (((x/2 - 1/2) * 1/2 - 1/2) * 1/2 - 1/2)
= ((x/2 - 1/2)/2 - 1/2) * 1/2 - 1/2
= ((x/2 - 1/2)/(2/2) - 1/2) * 1/2 - 1/2
= ((x/2 - 1/2) - 1/2) * 1/2 - 1/2
= (x/2 - 1/2 - 1/2) * 1/2 - 1/2
= (x/2 - 1) * 1/2 - 1/2
= (x/2 - 1)/2 - 1/2
= (x/4 - 1/2) - 1/2
= x/4 - 1/2 - 1/2
= x/4 - 1

Step 2: Substitute the simplified expression back into the equation.
1 = x/4 - 1

Step 3: Add 1 to both sides of the equation to isolate x/4.
1 + 1 = x/4
2 = x/4

Step 4: Multiply both sides of the equation by 4 to solve for x.
2 * 4 = x
8 = x

Thus, the initial number of marbles in the bag is 8.