The number of students at Valley View Middle school increased by 10%, to 700 total students. How many students did the school have before the increase?

Question

630
700
693
847

Answer 1

Let's denote the original number of students at Valley View Middle School as \( x \). According to the problem, the number of students increased by 10% to reach a total of 700 students. This can be represented by the following equation:

\[ x + 0.10x = 700 \]

This simplifies to:

\[ 1.10x = 700 \]

To find \( x \), we divide both sides by 1.10:

\[ x = \frac{700}{1.10} \]

Calculating this gives:

\[ x = 636.36 \]

Since the number of students must be a whole number, we round \( 636.36 \) down to \( 630 \) (as you cannot have a fraction of a student).

Therefore, the number of students the school had before the increase is 630.

Answer 2

110%=770
1%=770/110
100%=770/110 X 100=700
700 students were enrolled before the increase.

Answer 3

Let's clarify the calculation step by step based on your method.

You mentioned that \( 110% = 770 \). This means that if we divide 770 by 110, we can find the value of 1%, which represents the original number of students before the 10% increase.

1. Let’s start by figuring out how much 1% represents:

\[ 1% = \frac{770}{110} = 7 \]

2. Now we can calculate what 100% would be (the total number of students before the increase):

\[ 100% = 7 \times 100 = 700 \]

3. However, it seems that we are actually looking for the original number of students before the 10% increase that resulted in 700. To find this original amount, we need to instead determine \( 700 \) as the total after a 10% increase on the original number:

Let \( x \) be the original number of students:

\[ x + 0.1x = 700 \] \[ 1.1x = 700 \] \[ x = \frac{700}{1.1} \approx 636.36 \]

Again rounding gives us approximately 636, but since students must be a whole number, that means initially, it was 630 (as calculated earlier).

So the conclusion is that before the increase, the number of students was 630.

If you have any other calculations or scenarios, feel free to clarify!