The math club sold roses and tulips this year for valentines day. the number of roses sold was 8 more than 4 times the number of tulips sold. tulips were sold for $2 each and roses for $5 each. the club made $414.00. how many roses were sold?

In this question there are several information's of immense importance. They can be used to get the required answer. It is given that the Math Club sold 8 more roses than 4 times the number of tulip[s. The cost of each Tulip was $2 and the cost of each rose was $5. Total amount gained is $414.
Now
Let us assume the number of roses sold = x
Number of Tulips sold = y
Then
x = 8 + 4y
5x + 2y = 414
Now if we replace the value of x from the first equation to the second equation we get:
5x + 2y = 414
5(8 + 4y) + 2y = 414
40 + 20y + 2y = 414
22y = 414 - 40
22y = 374
y = 374/22
  = 17
Now putting the value of y in the first equation we get:
x = 8 + 4y
  = 8 + 4(17)
  = 8 + 68
  = 76
So the Math Club sold 76 roses and 17 tulips.