Question

A patient goes to the orthodontist because his teeth are 7 millimeters off the centerline to the left. After 4 months of treatment, his teeth have moved 3 millimeters to the right. What is the percent of change that has occurred in the 4 months?

Answer 1

The percent of change that has occurred in the 4 months is 142.86%.

Step-by-step explanation:

To calculate the percent of change, we need to find the ratio of the change in position to the original position and then multiply by 100 to express it as a percentage.

The original position is 7 millimeters to the left, and after 4 months it has moved 3 millimeters to the right. The change in position is 7 + 3 = 10 millimeters.

So, the percent of change is (10 / 7) * 100 = 142.86% (rounded to two decimal places).

Answer 2

The percentage of change that has occurred in the four months is approximately 42.857%.

Step-by-step explanation:

The general formula we can employ to answer this kind of question is

`\\ (change)/(starting\;point)*100\%`[1]

Then, we need to determine, firstly, what has been the change in these four months? It has been 3 millimeters to the right, or, in other words, the teeth are
`\\ 7 - 3 = 4` millimeters off the center-line to the left.

In other words, four months before it was 7 millimeters off the center-line to the left. Four month later, it is 4 millimeters off the center-line to the left (because it moved 3 millimeters to the right). So, the change is the difference between these two measures.

The initial or starting point is 7 millimeters.

Therefore, using [1]

`\\ (7-4)/(7)*100\%`

`\\ (3)/(7)*100\%`

`\\ 0.42857*100\%`

`\\ 42.857\%`

That is, the percentage of change that has occurred in the four months is approximately 42.857%.

Notice that directly using the experimented change by the teeth after the treatment, that is, 3 millimeters, we have the same result:

`\\ (3)/(7)*100\% = 42.857\%`