In a certain math class, each student has a text book, every 2 students share a book of tables, every 3 students share a problem book, and every 4 students share a mathematics dictionary. If the total number of books is 75..
how many students are in a class?
how many students share tables?
how many students share a problem book?
how many students share a math dictionary?
write the equattion
solve the equation
find the solution
answer each question
In a certain math class, each student has a text book, every 2 students share a book of tables, every 3 students share a problem book, and every 4 students share a mathematics dictionary. If the total number of books is 75..
how many students are in a class?
how many students share tables?
how many students share a problem book?
how many students share a math dictionary?
write the equattion
solve the equation
find the solution
answer each question
what is y=2x+6y=10
y=2x+6y=10
To solve this problem, let's assign variables to the unknown quantities:
Let's say there are "x" students in the class.
Now let's find the number of books each student has.
1. Every student has a textbook, so there are "x" textbooks in total.
2. Every 2 students share a book of tables. Since there are "x" students, the number of books of tables is "x/2".
3. Every 3 students share a problem book. The number of problem books is "x/3".
4. Every 4 students share a math dictionary. The number of math dictionaries is "x/4".
The total number of books is given as 75. So we can write the equation:
x + (x/2) + (x/3) + (x/4) = 75
Multiplying through by the least common multiple of 2, 3, and 4 (which is 12) to eliminate the fractions, we get:
12x + 6x + 4x + 3x = 900
Simplifying the equation, we have:
25x = 900
Now we can solve for "x" by dividing both sides of the equation by 25:
x = 900/25
x = 36
Therefore, there are 36 students in the class.
To find the number of students sharing tables, problem books, and math dictionaries, we substitute the value of "x" into the corresponding equations:
1. Number of students sharing tables: x/2 = 36/2 = 18 students.
2. Number of students sharing a problem book: x/3 = 36/3 = 12 students.
3. Number of students sharing a math dictionary: x/4 = 36/4 = 9 students.
So, the answers to the questions are:
- There are 36 students in the class.
- 18 students share tables.
- 12 students share a problem book.
- 9 students share a math dictionary.