First, let find the equation for one variable using the given information:
1)There were 24 fewer 2 lb boxes of walnuts than 3 lb boxes of pecans.
Set w for the boxes of walnuts.
Set p for the boxes of pecans.
Then, we can write the next equation:
w= p-24
Now, let's find the weight equation:
2)The total weight of the shipment was 462 lb.
(in a shipment of 3 lb boxes of pecans and 2 lb boxes of walnuts)
Therefore, we can write the next equation:
boxes of walnuts + boxes of pecans = 462 lb
2w + 3p = 462 lb
Replace using the first equation w= p-24
2(p -24)+3p = 462 lb
2p - 48 + 3p = 462 lb
Solve for p:
5p - 48 = 462
5p=462 + 48
5p =510
p = 510/5
p = 102
Hence, there are 102 boxes of pecans
and the total weight of pecans is given by "shipment of 3 lb boxes of pecans"
Then , 3p = 3(102)=306
To find the number of walnuts, replace p on the w equation:
w = p - 24
w= 102 - 24
w=78
There are 78 boxes of walnuts.
The weight is given by 2w = 2(78) =156 lb
