Final answer:
The cost of diamonds at different carats can be calculated by dividing the cost of a 3-carat diamond ($4,050) by 3. This makes the cost per carat $1,350, which we then multiply by the desired carat weight to find the costs for 1, 2, and 5 carats.
Step-by-step explanation:
To determine the cost of 1, 2, and 5-carat diamonds using the information that a 3-carat diamond costs $4,050, we'll assume that price scales linearly with carat weight (which is a simplification for the purpose of this exercise).
If a 3-carat diamond costs $4,050, then each carat costs $4,050 / 3 = $1,350.
Therefore, a 1-carat diamond would cost 1 x $1,350 = $1,350.
A 2-carat diamond would cost 2 x $1,350 = $2,700.
Similarly, a 5-carat diamond would cost 5 x $1,350 = $6,750.
This simple double number line would look like:
1 carat = $1,350
2 carats = $2,700
3 carats = $4,050
5 carats = $6,750