A florist had 66 more stalks of roses than tulips. She sold 1/3 of the roses and 3/5 of the tulips. She sold 74 more tulips than roses.
How many roses and tulips did she have left?
Thanks for your help.
r = t+66
(1/3 r) + 74 = 3/5 t
r = 426 and t = 360
So finish it off
Could you please tell me where r=426? and t=360 come from?
solve those two equations!
(1/3 r) + 74 = 3/5 t
multiply by 15 to clear fractions
5r + 15*74 = 9t
9t-5r = 1110
r = t+66, so
9t-5(t+66) = 1110
4t-330 = 1110
4t = 1440
t = 360
Got it!! Thanks :)
To solve this problem, let's break it down step by step.
Step 1: Let's assign variables to the unknowns. Let's say the number of roses is "r" and the number of tulips is "t".
Step 2: According to the problem, the florist had 66 more stalks of roses than tulips, so we can write the equation:
r = t + 66
Step 3: The florist sold 1/3 of the roses, so the number of roses remaining is 2/3 of the original number:
r_remaining = (2/3) * r
Step 4: The florist sold 3/5 of the tulips, so the number of tulips remaining is 2/5 of the original number:
t_remaining = (2/5) * t
Step 5: According to the problem, the florist sold 74 more tulips than roses, so we can write the equation:
t_remaining = r_remaining + 74
Step 6: Now we can substitute the values from step 3 and step 4 into step 5:
(2/5) * t = (2/3) * r + 74
Step 7: Multiply both sides of the equation by 15 (the least common denominator of 5 and 3) to eliminate fractions:
6t = 10r + 1110
Step 8: Rearrange the equation:
6t - 10r = 1110
Step 9: Substitute the value of r from step 2 into the equation:
6t - 10(t + 66) = 1110
Step 10: Simplify the equation:
6t - 10t - 660 = 1110
Step 11: Combine like terms:
-4t - 660 = 1110
Step 12: Add 660 to both sides of the equation:
-4t = 1770
Step 13: Divide both sides of the equation by -4:
t = -1770 / -4
t = 442.5
Since we cannot have partial stalks of tulips, this means there was an error in the problem, as the number of tulips should be a whole number. Please recheck the problem statement and provide the correct information.
If you have any other questions, feel free to ask!