Question

Draw and use a tape diagram to model and solve the problem below.

The number of students at Valley View Middle School increased by 10%, to 770 total students. How many students were enrolled at Valley View Middle School before the increase?
A.
630
B.
847
C.
693
D.
700
Reset Submit

Answer 1

To solve the problem of how many students were enrolled at Valley View Middle School before the 10% increase, we can use a tape diagram to represent the information visually.

### Tape Diagram:

1. **Initial Number of Students (before the increase)**: Let's call the original number of students \( x \).
2. **Increase**: The number of students increased by 10%, which means the new number of students is \( x + 0.10x = 1.10x \).
3. **Total Students after Increase**: We know this total is 770.

The tape diagram would have one section representing the original number of students (before increase), and a second section representing the 10% increase (which is 0.10x). Together, these two sections equal the total number of students:

\[
x + 0.10x = 770
\]

### Solve for \( x \):

To find the original number of students \( x \):

\[
1.10x = 770
\]

Now, divide both sides by 1.10:

\[
x = \frac{770}{1.10}
\]
\[
x = 700
\]

Thus, the original number of students enrolled at Valley View Middle School before the increase was **700**.

### Conclusion:
The answer is **D. 700**.