# 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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