The math club sold roses and tulips this year for Valentine's day. The number of roses sold was 8 more and 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?

76 roses were sold.

Step-by-step explanation:

Let x represent the number of tulips that the math club sold.

Let y represent the number of roses that the math club sold.

The number of roses sold was 8 more than 4 times the number of tulips sold. This means that

y = 4x + 8

Tulips were sold for $2 each and roses for $5 each. The club made $414.00. This means that

2x + 5y = 414- - - - - - - - - 1

Substituting y = 4x + 8 into equation 1, it becomes

2x + 5(4x + 8) = 414

2x + 20x + 40 = 414

22x = 414 - 40

22x = 374

x = 374/22

x = 17

y = 4x + 8 = 4 × 17 + 8

y = 76

76 roses were sold

Step-by-step explanation:

Let Rose be R, and Tulip be T

From the question, 2 equations were generated:

4T + 8 = Requation 1

On the cost of Rose and Tulip:

5R + 2T = 414equation 2

Substitute equation 1 into 2

5( 4T + 8) + 2T = 414

20T + 40 + 2T = 414

Combine like terms

20T + 2T = 414 - 40

22T = 374

Divide both sides by 22 to get T

T= 374/22

T= 17

now that we have T, substitute T into equation 1 to get R

4 (17) + 8 = R

68 + 8 = 76

R= 76

Check:

76 roses at $5 = $380

17 tulips at $2 = $34

Roses + Tulip = $414

I hope this helps.