SOLUTION: A fruit grower use two types of fertilizer in his orange grove, brand A and brand B. Each bag of brand A contains 9 pounds of nitrogen and 5 pounds of phosphoric acid. Each bag of

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A fruit grower use two types of fertilizer in his orange grove, brand A and brand B. Each bag of brand A contains 9 pounds of nitrogen and 5 pounds of phosphoric acid. Each bag of       Log On


   

Question 1073378: A fruit grower use two types of fertilizer in his orange grove, brand A and brand B. Each bag of brand A contains 9 pounds of nitrogen and 5 pounds of phosphoric acid. Each bag of brand B contains 8 pound of nitrogen and 6 pounds of phosphoric acid. Test indicate that the grove needs 770 pounds of nitrogen and 490 pounds of phosphoric acid. How many bags of each brand should be used to provide the required amounts of nitrogen and phosphoric acid.
I set up the equation with this:
9a + 8b=770
5a + 6b=490
I then took equation #2 and times it by 2, then subtracted equation #1 from equation #2...
Help at a loss..
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
.
You have this system

9a + 8b = 770      (1)
5a + 6b = 490      (2)

Multiply eq(1) by 5 (both sides). Multiply eq(2) by 9 (both sides). You will get

45a + 40b = 3850   (1')
45a + 54b = 4410   (2')

Now subtract eq(1') from eq(2'). You will get

54b - 40b = 4410 - 3850,   or

14b = 560   --->  b = 560%2F14 = 40.

From this point please complete the solution on your own.

The method I used is called the "Elimination method".


On solving systems of two linear equations in two unknowns (Algebra-I curriculum) see the lesson
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Solution of the linear system of two equations in two unknowns using determinant
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".



Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
If you are trying to use Elimination Method, factor of 2 seems not to be a useful choice.

system%289a%2B8b=770%2C5a%2B6b=490%29

Maybe try to eliminate terms of b.
8*3=24,and,6*4=24.


system%283%289a%2B8b%29=3%2A770%2C4%285a%2B6b%29=4%2A490%29

system%2827a%2B24b=2310%2C20a%2B24b=1960%29
Here, subtract equation #2 from #1.

7a=2310-1960
7a=350
highlight%28a=50%29

Now maybe you can find how to solve for b on your own. If you do this through Elimination, go back to the original system of equations and work from there.