Question

There are a total of
500
500 students in grades
1
1 through
5
5 in an elementary school.

​

17
%
17% of the total number of students are in
1
1st grade.
19
%
19% of the total number of students are in
4
4th grade.
The number of
3
3rd-grade students is
9
9 less than the number of
4
4th-grade students.
The number of
2
2nd-grade students is
10
10 less than the number of
5
5th-grade students.
​
Complete the table to show the number of students in each grade. Enter your answers in the table.

​

Answer 1

To find the number of students in each grade, let's represent the number of students in each grade as follows:

- 1st grade: \( G_1 \)
- 2nd grade: \( G_2 \)
- 3rd grade: \( G_3 \)
- 4th grade: \( G_4 \)
- 5th grade: \( G_5 \)

From the problem, we know:

1. The total number of students is \( 500 \).
2. \( 17\% \) of the students are in 1st grade:
\[
G_1 = 0.17 \times 500 = 85
\]

3. \( 19\% \) of the students are in 4th grade:
\[
G_4 = 0.19 \times 500 = 95
\]

4. The number of 3rd-grade students is \( 9 \) less than the number of 4th-grade students:
\[
G_3 = G_4 - 9 = 95 - 9 = 86
\]

5. The number of 2nd-grade students is \( 10 \) less than the number of 5th-grade students:
\[
G_2 = G_5 - 10
\]

Now, we can create the equation for the total number of students:
\[
G_1 + G_2 + G_3 + G_4 + G_5 = 500
\]
Substituting the known values:
\[
85 + G_2 + 86 + 95 + G_5 = 500
\]
Simplifying:
\[
266 + G_2 + G_5 = 500
\]
This leads to:
\[
G_2 + G_5 = 500 - 266 = 234
\]

Now, substituting \( G_5 \) in terms of \( G_2 \):
From the previous equation, we have:
\[
G_5 = G_2 + 10
\]

Substituting \( G_5 \) in our equation:
\[
G_2 + (G_2 + 10) = 234
\]
This simplifies to:
\[
2G_2 + 10 = 234
\]
\[
2G_2 = 234 - 10 = 224
\]
\[
G_2 = \frac{224}{2} = 112
\]

Now, substituting \( G_2 \) back to find \( G_5 \):
\[
G_5 = G_2 + 10 = 112 + 10 = 122
\]

Now, we can summarize the number of students in each grade:

- \( G_1 = 85 \) (1st grade)
- \( G_2 = 112 \) (2nd grade)
- \( G_3 = 86 \) (3rd grade)
- \( G_4 = 95 \) (4th grade)
- \( G_5 = 122 \) (5th grade)

Here's the final table:

| Grade | Number of Students |
|-------|--------------------|
| 1st | 85 |
| 2nd | 112 |
| 3rd | 86 |
| 4th | 95 |
| 5th | 122 |
| **Total** | **500** |