there are between 50 and 60 number of eggs in a basket. when loza counts by 3's there are 2 eggs left over, when she counts by 5's there are 4 eggs left over. How many eggs are there in the basket?

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  1. "..counts by 3's there are 2 eggs left over":
    5 8 11 .... 50 53 56 59 ....
    when she counts by 5's there are 4 eggs left over:
    9 14 19 ... 49 54 59 ....


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  2. Answer It

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  3. let (x,y) be eggs. then we have two expression.
    Notes : 5y+4=3x+2 cause in both side we get same amount of eggs.
    y=(17,18,19) are possible values.
    x=(10,11) are possible values.
    look! in order to get equal value of
    (5y+4=3x+2) y and x must be 11 and 19 respectively. So the total number of eggs in the basket is

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  4. 59

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  5. 1.first we must putout the number between 50 and 60.remember the question says (BETWEEN).
    that is(51,52,53,54,55,56,57,58,59).
    []the first statement says that,shortly 3X+2.before we do which number can be divided by 3 in the above, (51,54,57) can be divided by 3.
    these numbers must be equal to 3X.
    51=3x 54=3X 57=3X solve it.the answer is (17.18,19) respectively
    []the second statement says that,shortly 5Y+4.before we do which number can be divided by 5 in the above,(55) can be divided by 5.
    this number must be equal to 5X.
    5Y=55 solve it. the answer is (11).
    now genarily, X=(17,18,19) for the first statement.
    now generaliy, y=(11) for the second statement.
    logically,time of two statement is different,that is (3S for the first,4S for the second).then,what ever the time is different.the number of eggs in both statement is equal.
    so, we conclude that (the number of eggs of the first statement ) =(the number of eggs of the second statement)
    3X+2 =5y+4
    which number of X value of the first statement and which value Y of the second statement can make this equation true.
    3(17)+2 =5(11)+4,can not make this equation true.
    3(18)+2=5(11)+4,can not make this equation true.
    when we substitute 3(19)+2=5(11)+4,can make this equation true.
    so, the answer of this question is 59.


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  6. 59

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  7. Nice work🤗🤗

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