Question

1. the table shows the weekly change in the price of one gram of copper for four weeks.

week	change in price ($)
2	+2.15
3	-0.25
4	+2.50

part 1

• by how much did the price of one gram of copper change from the beginning of week 1 to the end of week 4?

part 2

• did the price increase or decrease? how do you know?

part 3

• at the end of week 4, the price per gram of copper was $12.24. what was the price per gram at the beginning of week 1?

Explanation:

Part 1

Step 1: Sum the weekly changes

To find the total change from the beginning of week 1 to the end of week 4, we add the changes for each week: $-1.50 + 2.15 - 0.25 + 2.50$.

Step 2: Calculate the sum

First, $-1.50 + 2.15 = 0.65$. Then, $0.65 - 0.25 = 0.40$. Finally, $0.40 + 2.50 = 2.90$.

To determine if the price increased or decreased, we look at the total change calculated in Part 1. A positive total change means the price increased, a negative one means it decreased. Since the total change was $\$2.90$ (positive), the price increased.

Step 1: Let the initial price be \( x \)

Let \( x \) be the price per gram at the beginning of week 1. The price at the end of week 4 is \( x + (-1.50 + 2.15 - 0.25 + 2.50) = 12.24 \).

Step 2: Substitute the total change

We know from Part 1 that the total change is \( 2.90 \), so the equation is \( x + 2.90 = 12.24 \).

Step 3: Solve for \( x \)

Subtract \( 2.90 \) from both sides: \( x = 12.24 - 2.90 = 9.34 \).

Answer:

The price of one gram of copper changed by $\$2.90$ from the beginning of week 1 to the end of week 4.

Part 2