Question

Caroline is planting flowers in her garden. She plants her first 7 flowers in 4 minutes. After 12 minutes, she has planted 21 different flowers. Which equation represents this direct variation?

- a. \(y = \frac{1}{2}x\)
- b. \(y = 3x\)
- c. \(y = 5x\)
- d. \(y = 7x\)

Answer 1

The equation that represents the direct variation in the number of flowers planted is y = (7/4)x.

Step-by-step explanation:

To find the equation that represents the direct variation in the number of flowers planted, we need to compare the number of flowers and the time taken. From the information given, we know that Caroline plants 7 flowers in 4 minutes and 21 flowers in 12 minutes.

We can create a proportion using the number of flowers (y) and the time taken (x):

y/21 = x/12

To simplify the equation, we can cross multiply:

12y = 21x

Divide both sides of the equation by 12 to isolate y.

y = (21/12)x

Simplify the fraction:

y = (7/4)x

So, the equation that represents the direct variation is y = (7/4)x.