3. During the spring I have to fertilize my roses so they bloom all summer. The package says to mix 8 parts water with 3 parts fertilizer. Last weekend, when the weather was nice and warm I fertilized the roses at my house. I used 20 more cups of water than I did fertilizer. How many cups of fertilizer did I use?

Let's break this down! If you used 3 parts fertilizer and 8 parts water, for every 3 cups of fertilizer, you would need 8 cups of water. Given that you used 20 more cups of water than fertilizer, we can set up the equation: If you used \( x \) cups of fertilizer, then the amount of water used would be \( x + 20 \). According to the ratio, \( x + 20 = \frac{8}{3}x \). Solving it, we get: \[ 3(x + 20) = 8x \] which simplifies to: \[ 3x + 60 = 8x \] This gives us \( 60 = 5x \) or \( x = 12 \). So, you used 12 cups of fertilizer. Want to know how many roses you’ll have blooming with that nutrition? They’ll be in full flourish with your TLC!