Word Problem help please asap?

sami is a veterinarian at a zoo. Over a yr she treats 23 birds and raccoons w/ a total of 58 legs. HOw many birds does she treat? (Trying to help my kid w/math problem and I am having a brain moment can can't remember the formula to do this....)

Comments

  • Hello!

    There isn't a special formula for this kind of problem. But you can boil it down to a problem with two variables in two equations and solve them; with X the number of birds and Y the number of raccoons:

    equation 1: X + Y = 23 (The total number of animals is 23)

    equation 2: 2X + 4Y = 58 (There are 58 legs to be found, 2 on each bird and 4 on each raccoon)

    Then eliminate one variable (X in this case, but you could eliminate Y just as well) by transforming the first equation and inserting it in the second:

    X = 23 - Y inserted in 2X + 4Y = 58 gives you:

    2 x (23 - Y) + 4Y = 58

    46 - 2Y + 4Y = 58 |-46

    2Y = 12 |/2

    Y = 6 meaning there are 6 raccoons.

    use that in X = 23 - Y and you get

    X = 23 - 6 = 17 so there are 17 birds.

    Quick Test:

    17 birds x 2 legs = 34 legs

    plus 6 raccoons x 4 legs = 24 legs

    equals 58 legs in total.

    If all the equations confuse you, then I can offer a more visual approach for this problem:

    Suppose there were 23 two-legged creatures treated, then you would have 46 legs of the 58 covered. This means, there are 58 - 46 = 12 legs uncovered. Now you have to distribute these 12 leftover-legs on some two-legged creatures to make them four-legged ones. As you can add 2 legs per creature, there must be 12 / 2 = 6 four-legged animals.

    This leaves 23 - 6 = 17 two-legged birds plus 6 four-legged raccoons.

    Test:

    17 birds x 2 legs = 34 legs

    plus 6 raccoons x 4 legs = 24 legs

    equals 58 legs in total.

    Hope that helped, good luck in the future!

  • b + r = 23: eqn 1

    4b +2r = 58: eqn 2

    2b + 2r = 46: 2*eqn 1

    2b = 12: eqn2 - 2* eqn 1

    b = 6

    r = 23-6 = 17

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