Question

Edwin works at a fast-food restaurant. Every Tuesday and Friday, he helps unload a delivery truck. This table shows how many boxes of hamburger buns and how many boxes of potatoes he unloaded last week.

Table:
(Boxes of Buns, Potatoes, and Total Weight respectively)
Tuesday: 40, 35, 1,945
Friday: 60, 70, 3,530

What is the weight of each box?
A box of buns weighs
pounds and a box of potatoes weighs
pounds.

Answer 1

To find the weight of each box of hamburger buns and potatoes, we can use a system of equations based on the information provided.

Let's define:
- \( b \) = weight of each box of buns (in pounds)
- \( p \) = weight of each box of potatoes (in pounds)

From the table:
1. On Tuesday, Edwin unloaded 40 boxes of buns and 35 boxes of potatoes with a total weight of 1,945 pounds:
\[
40b + 35p = 1945 \quad (1)
\]

2. On Friday, he unloaded 60 boxes of buns and 70 boxes of potatoes with a total weight of 3,530 pounds:
\[
60b + 70p = 3530 \quad (2)
\]

Now we have the following two equations to solve:

\[
40b + 35p = 1945 \tag{1}
\]
\[
60b + 70p = 3530 \tag{2}
\]

We can simplify equation (2) by dividing everything by 10:

\[
6b + 7p = 353 \tag{3}
\]

Now, we will solve equations (1) and (3) together. First, let's multiply equation (1) by 6 and equation (3) by 4 to align the coefficients of \( b \):

\[
240b + 210p = 11670 \tag{4} \quad (from \, equation \, 1)
\]
\[
24b + 28p = 1412 \tag{5} \quad (from \, equation \, 3)
\]

Next, we can multiply equation (5) by 10 to further align coefficients for subtraction:

\[
240b + 280p = 14120 \tag{6}
\]

Now we will subtract equation (4) from equation (6):

\[
(240b + 280p) - (240b + 210p) = 14120 - 11670
\]

This simplifies to:

\[
70p = 2450
\]

Solving for \( p \):

\[
p = \frac{2450}{70} = 35
\]

Now we have \( p = 35 \) pounds for each box of potatoes. We can substitute \( p \) back into equation (1) to find \( b \):

\[
40b + 35(35) = 1945
\]
\[
40b + 1225 = 1945
\]
\[
40b = 1945 - 1225
\]
\[
40b = 720
\]
\[
b = \frac{720}{40} = 18
\]

So, the weights of the boxes are:
- A box of buns weighs **18 pounds**.
- A box of potatoes weighs **35 pounds**.