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?

Respuesta :

Answer:

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

[tex] \\ \frac{change}{starting\;point}*100\%[/tex][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 [tex] \\ 7 - 3 = 4[/tex] 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]

[tex] \\ \frac{7-4}{7}*100\%[/tex]

[tex] \\ \frac{3}{7}*100\%[/tex]

[tex] \\ 0.42857*100\%[/tex]

[tex] \\ 42.857\%[/tex]

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:

[tex] \\ \frac{3}{7}*100\% = 42.857\%[/tex]