To answer this problem, you should set up a system of inequalities to model the total number of courses and credits. This would look like:
x+y=49
3x+4y=161
where x is the 3 credit courses and y is the 4 credit courses.
There are many ways to solve system of equation, but this would best be solved by the substitution method. On the first equation, subtract x from both sides to get y=49-x. Now, since we know what y equals, when can substitute "49-x" for y in the second equation and solve for x.
3x+4(49-x)=161
*Use the distributive property*
3x+196-4x=161
*Combine like terms*
-x+196=161
*Subtract 196 from both sides*
-x=-35
*Divide both sides by -1*
x=35
Now, that we know that the swim team took 35 3 credit courses, we can solve for y using the first equation.
*Plug in 35 for x*
35+y=49
*Subtract 35 from both sides*
y=14
The swim team took 35 3 credit courses and 14 4 credit courses.
Hope this helps!
