SOLUTION: I am a sophomore in high school and am taking Algebra II. Right now we are reviewing Algebra I stuff and I honestly don't remember much about word problems and I have never been go

Question 569414: I am a sophomore in high school and am taking Algebra II. Right now we are reviewing Algebra I stuff and I honestly don't remember much about word problems and I have never been good at them. For this problem I have to solve by writing systems of equations.. I just don't know how to get equations out of word problems..
please help?
"For a mathematics project, 26 students were divided into four groups. Two groups had the same number of student. The other two groups each had one more studen than the smaller groups. How many students were in the smaller group?"

also..
"When she graduated fom college, Regina was offered two jobs. One paid a starting salary of $30,000 annually, plus guaranteed increases of $2,000 per year. The other paid a starting salary of $25,000 annually, plus guaranteed increases of $3,000 per year. After how many year would the salaries be equal?"

Im not looking for the answers I am just looking for someone to explain how to set up the system of equations for these problems I can answer them after I get the equations!!!(:
please and thank you!!!
~J
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
"For a mathematics project, 26 students were divided into four groups.
G1 + G2 + G3 + G4 = 26
-------------------------------------
Two groups had the same number of student.
Let G1 and G2 have "x" students.
-------------------------------------
The other two groups each had one more student than the smaller groups.
Then G3 and G4 must have "x+1" students.
---------
How many students were in the smaller group?"
-----------------------
Equation:
x + x + x+1 + x+1 = 26
4x + 2 = 26
4x = 24
x = 6 (# of students in the smaller group).
==============
also..
"When she graduated fom college, Regina was offered two jobs.
One paid a starting salary of $30,000 annually, plus guaranteed increases of $2,000 per year.
S1 = 30000 + 2000x for x = 1,2,3...
--------------------------
The other paid a starting salary of $25,000 annually, plus guaranteed increases of $3,000 per year.
S2 = 25000 + 3000x for x = 1,2,3...
--------------------------------
After how many years would the salaries be equal?"
Equation:
Solve: S1 = S2
30000 + 2000x = 25000 + 3000x
1000x = 5000
x = 5 years
================
Cheers,
Stan H.
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