SOLUTION: Maurice is looking at his options for colleges. He can only borrow 12,570 a year for tuition. The community college in town does not offer every class he needs, and he cannot affor

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Question 1163229: Maurice is looking at his options for colleges. He can only borrow 12,570 a year for tuition. The community college in town does not offer every class he needs, and he cannot afford to attend the university full time. The university charges 3500 per credit hour (u) and the community college charges 230 per credit hour (c). In order to finish his degree on time, maurice take 12 credit hours per semester for both fall and spring semesters but not for the summer semester.
Use the variables u and c to set up two equations to solve the given problem.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

This many-words problem is reduced to two equations


        u +    c =    12   credit hours     (1)

    3500u + 230c = 12570   dollars          (2)


Thus the setup is done.


There are several different methods to solve this system.

In my solution, I will use the substitution method.



From equation (1), express  c = 12-u  and substitute it into equation (2).
You will get then

    3500u + 230*(12-u) = 12570

    3500u + 230*12 - 230u = 12570

    3270u = 12570 - 230*12

    3270u =  9810

        u =  = 3.


ANSWER.  3 credit hours from the university, and the rest, 12-3 = 9 credit hours from the community college.


CHECK.   3*3500 + 9*230 = 12570 dollars.    ! Correct !

Solved.

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On solving systems of linear equations in two unknowns see the lessons
    - Solution of a linear system of two equations in two unknowns by the Substitution method
    - Solution of a linear system of two equations in two unknowns by the Elimination method
    - Solution of a linear system of two equations in two unknowns using determinant
    - Geometric interpretation of a linear system of two equations in two unknowns
    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method
    - Solving word problems using linear systems of two equations in two unknowns
in this site.


To see many typical word problems solved using systems of linear equations and to learn on how to setup them, see the lessons
    - Word problems that lead to a simple system of two equations in two unknowns
    - Oranges and grapefruits
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
    - Using systems of equations to solve problems on shares
    - Using systems of equations to solve problems on investment
    - Two mechanics work on a car
    - The Robinson family and the Sanders family each used their sprinklers last summer
    - Roses and vilolets
    - Counting calories and grams of fat in combined food
    - A theater group made appearances in two cities
    - HOW TO algebreze and solve this problem on 2 equations in 2 unknowns
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



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