Find the total weight of the boxes of pecans in a shipment of 3 lb boxes of pecans and 2 lb boxes of walnuts. 1)there were 24 fewer 2 lb boxes of walnuts than 3 lb boxes of pecans. 2)The total weight of the shipment was 462 lb.
How do I set this up in a chart?
To set up this problem in a chart, you can create a table with two columns: one for the number of boxes and one for the weight.
Let's assign variables to the unknowns:
Let P represent the number of 3 lb boxes of pecans.
Let W represent the number of 2 lb boxes of walnuts.
So, our chart will look like this:
| Number of Boxes | Weight per Box |
|-----------------|----------------|
| P | 3 |
| W | 2 |
Now, let's fill in the information given:
1) "There were 24 fewer 2 lb boxes of walnuts than 3 lb boxes of pecans."
This statement can be represented as: W = P - 24
2) "The total weight of the shipment was 462 lb."
The total weight equation can be written as: 3P + 2W = 462
Now you can add these equations to the table:
| Number of Boxes | Weight per Box |
|-----------------|----------------|
| P | 3 |
| W | 2 |
And the additional equations:
| Number of Boxes | Weight per Box |
|-----------------|-----------------|
| P | 3 |
| W | 2 |
| W = P - 24 | |
| 3P + 2W = 462 | |
Now you have set up the problem in a chart format.
To set up the problem in a chart, you can create a table with two columns: one for the number of boxes and one for the weight of each type of nut. Here's how you can set it up:
Type of Nut | Number of Boxes | Weight per Box
------------|----------------|----------------
Pecans | | 3 lb
Walnuts | | 2 lb
Now, let's fill in the information given in the problem:
1) "There were 24 fewer 2 lb boxes of walnuts than 3 lb boxes of pecans":
Let's assume there are 'x' 3 lb boxes of pecans. According to the given information, the number of 2 lb boxes of walnuts would be 'x - 24'.
Type of Nut | Number of Boxes | Weight per Box
------------|----------------|----------------
Pecans | x | 3 lb
Walnuts | x - 24 | 2 lb
2) "The total weight of the shipment was 462 lb":
The total weight of the pecans can be calculated by multiplying the number of boxes (x) by the weight per box (3 lb). The total weight of the walnuts can be calculated by multiplying the number of boxes (x - 24) by the weight per box (2 lb). Adding these two weights should equal 462 lb.
3 * x + 2 * (x - 24) = 462
This equation can be solved to find the value of x, which represents the number of 3 lb boxes of pecans. Once you solve for x, you can then calculate the number of 2 lb boxes of walnuts (x - 24) and the weight of each type of nut by multiplying the appropriate variables.