Question 1154316
Let us say he uses x old packages and y new packages.

x old packages will have 
40x pounds of supplement and 70x pounds of weed killer.

y new packages will have 
55y pounds of supplement and 55y pounds of weed killer.

Total supplement in the mixture should be 3125
ie {{{40x + 55y = 3125}}} --- (1)

Total weedkiller in the mixture should be 4025
ie {{{70x + 55y = 4025}}} --- (2)

We need to solve the two simultaneous equations above. Since the coefficient of y is 55 in both the equations, it makes it easy to solve!

Subtract (1) from (2) to get
{{{70x - 40x + 55y - 55y = 4025 - 3125}}}


Simplifying
{{{30x = 900}}} or {{{x = 30}}}
Substituting for x in (1) we get

{{{40*30 + 55y = 3125}}} or

{{{55y = 3125 - 1200 = 1925}}} or

{{{y = 1925/55 = 35}}}

So he needs 30 old packages and 35 new packages

Check:
30 old packages will give
30*40 supplement and 30*70 weed killer
i.e. 1200 pounds supplement and 2100 pounds weed killer

35 new packages will give
35*55 supplement and 35*55 weed killer
i.e. 1925 pounds supplement and 1925 pounds weed killer

Total supplement = 1200 + 1925 = 3125
Total weed killer = 2100 + 1925 = 4025
Check successful!

<b> Ans: 30 old packages, 35 new packages </b>