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

• by how much did the price of one gram of copper change from the beginning of week 1 to the end of week 4?
• did the price increase or decrease? how do you know?
• 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:

First Sub - Question: By how much did the price of one gram of copper change from the beginning of week 1 to the end of week 4?

Step 1: Identify the changes each week

The changes in price per week are: Week 1: $- 1.50$, Week 2: $+2.15$, Week 3: $- 0.25$, Week 4: $+2.50$.

Step 2: Sum the changes

To find the total change, we add all the weekly changes together. So we calculate $(-1.50)+(2.15)+(-0.25)+(2.50)$.
First, add $- 1.50$ and $2.15$: $-1.50 + 2.15=0.65$.
Then, add $-0.25$ to the result: $0.65-0.25 = 0.4$.
Finally, add $2.50$ to the result: $0.4 + 2.50=2.90$.

To determine if the price increased or decreased, we look at the total change we calculated in the first sub - question. The total change from the beginning of week 1 to the end of week 4 is $+ 2.90$ (a positive value). A positive change in price means that the final price is higher than the initial price.

Step 1: Let the initial price be $x$

Let $x$ be the price per gram of copper at the beginning of week 1. The total change in price from the beginning of week 1 to the end of week 4 is $\$2.90$ (from the first sub - question). The price at the end of week 4 is the initial price plus the total change. So we have the equation $x + 2.90=12.24$.

Step 2: Solve for $x$

To find $x$, we subtract $2.90$ from both sides of the equation: $x=12.24 - 2.90$.
Calculating $12.24-2.90 = 9.34$.

Answer:

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

Second Sub - Question: Did the price increase or decrease? How do you know?