Question

4) Find the total weight of the boxes of pecans in a shipment of 3 lb boxes of pecans and 2lb boxes of walnuts.There were 24 fewer 2 lb boxes of walnuts than 3 lb boxes of pecans.The total weight of the shipment was 462 lb.You can use the following chart to help you get started.Weight per boxNumer of boxesTotal WeightPecansWalnuts

Answer 1

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