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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?

Verified Answer :

W0lf93

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.

carlosego

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

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