Question

the teacher separated her class of twenty-eight student into two group. one group has 4 more than twice as many students as the other group. how many students are in each group?

Answer 1

There are 20 students in one group and 8 students in the other. To represent this as an equation, x + y = 28, where y = 2x + 4. Therefore, x + 2x + 4 = 28. 3x + 4 = 28. 3x = 24. x = 24/3. x = 8. Put the x value into the y equation and it gives you 20.

Answer 2

For this case, the first thing we must do is define variables:

x: students of group 1

y: students of group 2

We now write the system of equations that models the problem:

$x + y = 28\\y = 2x + 4$

Solving the system by substitution we have:

$x + (2x + 4) = 28\\3x + 4 = 28\\3x = 28-4$

$3x = 24$

$x = \frac{24}{3}\\x = 8$

Then, the value of y is given by:

$y = 2 (8) +4\\y = 16 + 4\\y = 20$

Answer:

8 students of group 1

20 students of group 2