SOLUTION: In a meadow filled with wildflowers, a hiker observes 450 butterflies. Scientists have been studying this meadow for years and have discovered that the number of butterflies de
Algebra ->
Equations
-> SOLUTION: In a meadow filled with wildflowers, a hiker observes 450 butterflies. Scientists have been studying this meadow for years and have discovered that the number of butterflies de
Log On
Question 1182658: In a meadow filled with wildflowers, a hiker observes 450 butterflies. Scientists have been studying this meadow for years and have discovered that the number of butterflies depends on the number of flowers in the field. The line of best-fit that they calculated is shown below. If the hiker's observation is analyzed, the residual for the number of butterflies is -27. How many flowers are there in the field?
Number of butterflies = 86+0.25(number of flowers Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem:
1. **Let 'f' represent the number of flowers.** The equation given is:
Number of butterflies = 86 + 0.25f
2. **The hiker observed 450 butterflies.** This is the *actual* (observed) number of butterflies.
3. **The residual is -27.** The residual is the difference between the actual value and the predicted value from the line of best fit. So:
Residual = Actual number of butterflies - Predicted number of butterflies
-27 = 450 - (86 + 0.25f)
4. **Solve for 'f' (number of flowers):**
-27 = 450 - 86 - 0.25f
-27 = 364 - 0.25f
0.25f = 364 + 27
0.25f = 391
f = 391 / 0.25
f = 1564
Therefore, there are **1564** flowers in the field.
