Can you help me with this algebra problem?This yer I'm going to be in preap algebra 1, so this summer I've been working on some problems our...

The trickiest part of this problem is transforming the
words into a mathematical equation. In our equations, we'll let P represent the number
of boxes of pecans, and W represent the number of boxes of
walnuts.

First, we know that there were 462 total pounds,
and each pecan box weighs 3 pounds, while walnuts weigh 2. This gives us the following
equation:

(1) 3P + 2W =
462

Next, we are told there are 24 fewer boxes of walnuts
than pecans, giving us the following equation:

(2) P  - W =
24.

We now have to equations and two unknows, so we can
proceed to solve for P and W. To do this, we'll start by rewriting (2) in terms of
P:

(3) P = 24 + W

We now plug
this value for P back into (1). This will give us an equation just in terms of W. We
will then solve for W

(4) 3(24 + W) + 2W =
462

=> 72 + 3W + 2W =
462

=> 72 + 5W =
462

=> 5W =
390

=> W = 78

We now
know that there are 78 total boxes of walnuts. Now that we know the total boxes of
walnuts, we can find pecans using (3):

P = 24 +
W

=> P = 24 + 78 =
102

We have now found that there were 102 boxes of pecans
and 78 boxes of walnuts.

But the problem was asking of for
the total weight of the boxes. Each pecan box weighs 3 pounds, and each walnut box
weight 2 pounds, so we can find this
easily:

Total weight of pecans = 102 * 3
= 306
lbs

Total weight of walnuts =
78 * 2 = 156 lbs