algebra I

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System of Equations

I need help with the following problem:

A youth group with 26 members is going skiing. Each of the five chaperones will drive a van or a sedan. The vans can seat 7 people and the sedans can seat five people. How many of each type of vehicle could transport all 31 people to the ski area in one trip?

I used the following equation:

7x + 5y = 31. (x= van, y=sedan)
7x=31-5y.
I divdied by 7 on both sides.
x=31-5y/7.

This is where I got stuck. What am I doing wrong?

  • algebra I -

    You have only one equation. You need another.
    x + y = 5 (vans + sedans = 5)
    Next, you make an error in your last statement.
    7x=31-5y so
    x = (31-5y)/7
    However, I would do it an easier way unless your teacher told you to solve by substitution. I would solve by elimination.
    x+y=5
    7x+5y=31
    ===============
    Multiply top equation by 7
    7x+7y=35
    7x+5y=31
    ===========
    Now subtract equation 2 from equation 1 to obtain
    2y=4 with y = 2, then solve for x.

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