SOLUTION: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of long-term growth supplement and 50 pounds of weed killer. The new packages

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of long-term growth supplement and 50 pounds of weed killer. The new packages      Log On


   

Question 1176875: A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of long-term growth supplement and 50 pounds of weed killer. The new packages contain 45 pounds of long-term growth supplement and 65 pounds of weed killer. Using past experiences, the farmer estimates that he needs 1350 pounds of long-term growth supplement and 1400 pounds of weed killer for the fields. How many old packages of fertilizer and how many new packages of fertilizer should he use?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the number of old packages and y = the number of new packages.

create a table as shown below: 

                                          x                y
description                              old              new         total

long term growth supplements              60               45          1350
weed killer                               50               65          1400


the two equations that need to be solved simultaneously are:

60x + 45y = 1350
50x + 65y = 1400

multiply both sides of the first equation by 5 and both sides of the second equation by 6 to get:

300x + 225y = 6750
300x + 390y = 8400

subtract the first equation from the second to get:

165y = 1650

solve for y to get:

y = 1650 / 165 = 10

solve for x in the first equation to get:

300x + 225 * 10 = 6750
solve for x to get:
x = (6750 - 2250) / 300 = 4500 / 300 = 15

you have x = 15 and y = 10

go back to the original equations and replace x and y with these values to get:

60x + 45y = 1350 becomes 60 * 15 + 45 * 10 = 1350 which becomes 900 + 450 = 1350 which becomes 1350 = 1350 which is true.

50x + 65y = 1400 becomes 50 * 15 + 65 * 10 = 1400 which becomes 750 + 650 = 1400 which becomes 1400 = 1400 which is true.

the values of x and y are confirmed to be good.

your solution is that he should use 15 old packages and 10 new packages.