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## SAT Ratio Proportion Percents: Arithmetic Word Problem

### Question 1: Word Problem : Numbers & Operations

If 3 students are made to sit in a row, then 9 students do not have a seat. Alternatively, if 9 students are made to sit in a row, then 5 rows are empty. How many students have to be seated in a row so that an equal number of students sit in all the rows and all the students are seated?

1. 5
2. 4
3. 8
4. 7
5. 6
Choice B. 4 students to each row.

This one is an arithmetic word problem. In SAT arithmetic word problems test your ability to translate information given in words to mathematical equations and expressions. A clue to crack the question is given in the first tab. Using the clue try and solve the question yourself. If you are not able to solve using the hint, click on the next tabs to get a 3 step explanation to this word problem.

### Clue to solve the question

Irrespective of the seating arrangement two things remain unchanged.

1. Number of rows in the classroom.
2. Total number of students in the class.

Equating the number of students in class when seated in arrangement 1 to that in arrangement 2 should get you the answer.

### Step 1: When seated as stated in Arrangement 1

Let the number of students in the class be 'n'

Let the number of rows in the classroom be 'r'

Arrangement 1: If 3 students are made to sit in a row, then 9 students do not have a seat.

3 students are made to sit in a row.

So, 3r students will be seated.

9 students do not have seats.

The total number of students in the class will be sum of those who are seated and those who do not have seats.

So, n = 3r + 9

### Step 2: When seated as stated in Arrangement 2

Arrangement 2: If 9 students are made to sit in a row, then 5 rows are empty.

Each row has 9 students. We know there are ‘r’ rows.

However, not all rows are occupied when each row accommodates 9 students. 5 rows are empty.

So, only (r – 5) rows are occupied.

So, number of students in the class = all students who have been seated.

i.e., n = 9(r – 5)

### Step 3: Equate the number of students obtained in Step 1 and Step 2

Arrangement 1: n = 3r + 9

Arrangement 2: n = 9(r - 5)

Equating the two we get 3r + 9 = 9(r – 5)

3r + 5 = 9r – 45

6r = 54

or r = 9

The number of rows in the classroom is 9.

Substitute r = 9 in the equation {n = 3r + 9} obtained in Step 1.

Number of students in the class = 3(9) + 9 = 27 + 9 = 36.

We need to find out the number of students to be seated per row if each row seated equal number of students.

36 students to be seated in 9 rows.

So, number of students per row = $36 \over 9 \\$

Number of students per row = 4.

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