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Math Help - Algebra

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    Algebra

    An electrical technician needs electrical tape and wire for his inventory. The tape costs $9 per package and the wire costs $6 per roll. Show the possible combinations of tape and wire he can purchase for less than $54.

    I have no clue how to solve this problem.
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    Super Member Aryth's Avatar
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    Quote Originally Posted by Shinjiro View Post
    An electrical technician needs electrical tape and wire for his inventory. The tape costs $9 per package and the wire costs $6 per roll. Show the possible combinations of tape and wire he can purchase for less than $54.

    I have no clue how to solve this problem.
    It's actually easier than you think.

    First, you can set up an inequality:

    x = tape
    y = wire

    9x + 6y < 54

    Now, we can see that how much of one thing will affect how much of the other you can obtain, so, we can solve for each independently and see what we can come up with:

    -First divide everything by 3:

    3x + 2y < 18

    Next, isolate either variable (I'm going to use y first).

    2y < 18 - 3x

    Divide by 2:

    y < 9 - \frac{3}{2}x

    This says that the number of packages of wire you can obtain is less than 9 - \frac{3}{2}x, so it is dependent on how many packages of tape you get.

    Let's go back to step one:

    3x + 2y < 18

    Now we isolate the other variable:

    3x < 18 - 2y

    Now we divide by 3:

    x < 6 - \frac{2}{3}y

    This tells you that the packages of tape must be less than 6 - \frac{2}{3}y.

    Therefore, all possible combinations of x and y are found in these two inequalities:

    x < 6 - \frac{2}{3}y

    y < 9 - \frac{3}{2}x

    It all depends on what you buy first.
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