Algebra word problem.

Question

Jan's commission for February was $15 more than one half her commission for March. her total commission for both months was $633. find her commission for each month.

Answer 1

Hi Kym,

 

Let's begin by assigning letters to represent our two unknowns:

    x = Jan's commission for February

    y = Jan's commission for March

 

Next, let's write two equations which we can use to solve for our two unknowns:

    Equation #1  [commission relationship]:

        x = y/2 + 15

    Equation #2  [total commission]:

        x + y = 633

 

Next, let's group our equations and solve for each unknown:

    x = y/2 + 15  [Equation #1]

    x + y = 633   [Equation #2]

    (y/2 + 15) + y = 633  [x in terms of y in #2 

                                    from #1]

    y/2 + 15 + y = 633

    2(y/2) + 2(15) + 2(y) = 2(633)

    y + 30 + 2y = 1266

    3y + 30 = 1266

    3y = 1266 - 30

    3y = 1236

    y = 1236/3

    y = $412 (Jan's commission for March)

    x + y = 633     [Equation #2]

    x + 412 = 633  [replace with y value]

    x = 633 - 412

    x = $221 (Jan's commission for February)

 

Finally, we can check our answers to see if they satisfy the given commission relationship using

Equation #1:

    x = y/2 + 15         [Equation #1]

    221 = 412/2 + 15  [answers plugged in]

    221 = 206 + 15

    221 = 221  [commission relationship satisfied]

 

Since our answers satisfied the given commission relationship, we are confident that our answers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.