Question 1176875
let x = the number of old packages and y = the number of new packages.


create a table as shown below:


<pre>
                                          x                y
description                              old              new         total

long term growth supplements              60               45          1350
weed killer                               50               65          1400
</pre>


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.