Question
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.
Answers
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
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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