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29 September, 13:50

A sporting goods store sells 3 fishing reels and 5 fishing rods for $309. Later, they sell 6 fishing reels and 2 fishing rods for $282 find the price of each item

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  1. 29 September, 15:39
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    X = reels

    y = rods

    so

    3x + 5y = 309

    6x + 2y = 282

    let's use equation 2 and get the y's on a side by themself by subtracting 6x from both sides

    6x + 2y - 6x = 282 - 6x

    becomes

    2y = 282 - 6x

    now divied both sides by 2

    y = (282 - 6x) / 2

    y = 141 - 3x

    now stick that y value into the first equation

    3x + 5y = 309

    becomes

    3x + 5 (141 - 3x) = 309

    multiply it out

    3x + 705 - 15x = 309

    -12x = 309 - 705

    -12x = - 396

    x = 33

    cost of each reel = 33

    now substitute 33 for x into equation 1 or equation 2 (it doesn't matter which) to find out the value of each rod using equation 1

    3x + 5y = 309

    3 (33) + 5y = 309

    99 - 309 = - 5y

    -210 = - 5y

    y = 42
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