Answer:
The number of Pencils purchased and the cost of pencils has a proportional relationship.
Explanation:
In order to figure out if a proportional relationship between two variable exists,
- All you need is to check if relationships between two variables have equivalent ratios.
- If the ratios between two variables is same, it means a proportional relationship between two variable exists.
Lets take a simple example:
As
2/10 = 9/45 is a TRUE proportion.
The reason is that both fractions reduces to 1/5, and
because 10 × 9 = 2 × 45.
So
In the equation it needs to be determined whether the number of Pencils purchased and the cost of pencils represent a proportional relationship?
When we are given that:
In other words each pencil costs $0.25.
As each pencil costs $0.25, it means:
2 pencils cost $0.5, 3 pencils cost $0.75, and 4 pencils cost $1 and so on.
Thus
Cost ÷ No of Pencils Purchased = 0.25 ÷ 1 = 0.5 ÷ 2 = 0.75 ÷ 3 = 1 ÷ 4
And the ratio is same.
i.e. cost per pencil = 0.25 : 1
As all of the ratios are same, we can determine that it has a proportional relationship.
Therefore, the number of Pencils purchased and the cost of pencils has a proportional relationship.