math

A florist had an equal number of red and yellow tulips. She sold 624 red tulips. Then she had 4 times as many yellow tulips as red tulips. How many tulips did she start with? You must use a bar model to solve this problem.

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  1. n = Number of tulips

    r = Number of red tulips

    y = Number of yelow tulips

    n = r + y

    A florist had an equal number of red and yellow tulips.

    r = y

    n = r + y = y + y = 2 y

    2 y = n Divide both sides by 2

    y = n / 2

    r = y

    r = n / 2

    After she sold 624 red tulips she had r - 624 = n / 2 - 624 red tulips

    She had unchanged number of yellow tulips y = n / 2

    Proportion :

    y / r = 4

    ( n / 2 ) / r = 4

    ( n / 2 ) / ( n / 2 - 624 ) = 4 Multiply both sides by 2

    n / ( n / 2 - 624 ) = 8 Multiply both sides by ( n / 2 - 624 )

    n = 8 * ( n / 2 - 624 )

    n = 8 * n / 2 - 8 * 624

    n = 4 n - 4992 Subtract n to both sides

    n - n = 4 n - 4992 - n

    0 = 3 n - 4992 Add 4992 to both sides

    0 + 4992 = 3 n - 4992 + 4992

    4992 = 3 n Divide both sides by 3

    4992 / 3 = 3 n / 3

    1664 = n

    n = 1664

    Proof :

    r = Number of red tulips

    y = Number of yelow tulips

    r = n / 2 = 1664 / 2 = 832

    y = n / 2 = 1664 / 2 = 832

    After she sold 624 red tulips she had 832 - 624 = 208 red tulips

    and

    y = n / 2 = 1664 / 2 = 832 yellow tulips

    y / r = 832 / 208 = 4

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