Help with this question please.

The number of Pencils purchased and the cost of pencils has a proportional relationship.

Step-by-step explanation:

In order to figure out if 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.

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step-by-step explanation: