SOLUTION: A 5 pound bag of grass seed covers 9,000 square feet. How many pounds would be needed to cover 32,000 square feet?

Algebra ->  Testmodule -> SOLUTION: A 5 pound bag of grass seed covers 9,000 square feet. How many pounds would be needed to cover 32,000 square feet?      Log On


   

Question 1200612: A 5 pound bag of grass seed covers 9,000 square feet. How many pounds would be needed to cover 32,000 square feet?
Found 3 solutions by ikleyn, greenestamps, MathTherapy:
Answer by ikleyn(52886) About Me  (Show Source):
You can put this solution on YOUR website!
.

Write a proportion as you read the problem

    5%2F9000 = x%2F32000.


From the proportion, find  x = %285%2A32000%29%2F9000 = %285%2A32%29%2F9 = 160%2F9 = 177%2F9 = 17.78 pounds  (rounded).    ANSWER

Solved.

------------------

For introductory lessons on proportions,  see the lessons
    - Proportions
    - Using proportions to solve word problems
    - Typical problems on proportions
    - Using proportions to estimate the number of fish in a lake
    - HOW TO algebraize and solve these problems using proportions
in this site.

Learn the entire subject from there.


Happy learning  ( ! )




Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a typical very formal solution using a proportion. That of course is one way to set up and solve the problem.

For a more informal solution, using logical reasoning, you can simply say that since the area increased by a factor of 32,000/9,000 = 32/9, the amount of grass seed required will increase by a factor of 32/9.

5%2832%2F9%29=160%2F9

ANSWER: 160/9 pounds, or 17.78 pounds (rounded)

You end up doing exactly the same calculation -- but the setup is faster and easier.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
A 5 pound bag of grass seed covers 9,000 square feet. How many pounds would be needed to cover 32,000 square feet?
With A being the amount needed to cover the 32,000 sq ft, set up a proportion, as follows: matrix%281%2C3%2C+5%2FA%2C+%22=%22%2C+%229%2C000%22%2F%2232%2C000%22%29
                                            matrix%281%2C3%2C+5%2FA%2C+%22=%22%2C+9%2F32%29 ------ Simplifying right-side fraction
                                            9A = 5(32) ---- Cross-multiplying
Amount needed to cover the 32,000 sq ft, or