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Math Help - An Algebra II Problem: Involving Gloves and Scarves I Have No Idea How to Do This

  1. #1
    Newbie stmsnyder1's Avatar
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    An Algebra II Problem: Involving Gloves and Scarves I Have No Idea How to Do This

    Hi,

    You're buying scarves and gloves, as gifts for family members. Each scarf costs $3 less than each pair of gloves. Each pair of gloves costs $9. You buy 8 items for $66. How many scarves did you buy?

    So, each scarf cost $6, Four scarves cost $24. Four pairs of gloves cost $36. That costs $60 total. I'm $6 short, but can only by 8 items.

    Thanks-
    Isabel
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  2. #2
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    9g + 6s = 66
    g + s = 8


    (-9)g + (-9)s = (-9)8
    -9g + -9s = -72

    Subtract 9g + 6s = 66
    -9g - 9s = -72
    -3s = -6
    s = 2
    Scarves = 2 therefore Gloves = 6








    6 Gloves and 2 Scarves
    Last edited by galanm; March 14th 2009 at 10:41 AM. Reason: better answer
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stmsnyder1 View Post
    Hi,

    You're buying scarves and gloves, as gifts for family members. Each scarf costs $3 less than each pair of gloves. Each pair of gloves costs $9. You buy 8 items for $66. How many scarves did you buy?

    So, each scarf cost $6, Four scarves cost $24. Four pairs of gloves cost $36. That costs $60 total. I'm $6 short, but can only by 8 items.

    Thanks-
    Isabel
    the numbers here are small enough to figure out by trial and error. but in case you can't, here's a way to solve for the answer.

    let s be the number of scarfs you buy. let g be the number of gloves you buy.

    since you buy 8 items in all, s + g = 8

    since each scarf costs $6 and each glove costs $9 and you spend $66 dollars in all, you have 6s + 9g = 66

    thus you have two simultaneous equations with two unknowns, you can solve for s
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