Let's say each bun box weighs b pounds and each potato box weighs p pounds. For each box of buns, we add b pounds. Therefore, for 40 boxes of buns, we add 40 * b pounds. Similarly, for 35 boxes of potatoes, we add 35 * p pounds.

For Tuesday, the total weight of the buns boxes is equal to 40 * b. The total weight of the potato boxes is equal to 35 * p. Adding these two together, we get the total weight of the boxes to be equal to

40 * b + 35 * p = 1945

For Friday, we can apply similar techniques to get

60 * b + 70 * p = 3530

We therefore have the two equations

40 * b + 35 * p = 1945

60 * b + 70 * p = 3530

One way to solve this would be to convert this into a matrix and use Guass-Jordan Elimination. With the amount of bun boxes representing the first column, the amount of potato boxes representing the second, and the total weight of each day representing the third, we have

$\left[\begin{array}{ccc}40&35&1945\\60&70&3530\end{array}\right]$

One thing that we can do here is multiply the first row by -2 and add it to the second. That way, there would be a 0 in the 2nd column in the 2nd row, making an equation of the form

something * b = something else, enabling us to solve for b.

We thus have

$\left[\begin{array}{ccc}40&35&1945\\(-40*2+60)&(-35*2+70)&(-1945*2 +3530)\end{array}\right] = \left[\begin{array}{ccc}40&35&1945\\-20&0&-360\end{array}\right]$

Therefore, we can say that

-20 * b = -360

divide both sides by 20 to isolate b

b = 18

Therefore, each box of bunds weighs 18 pounds. Plugging that into an equation, we have

40 * b + 35 * p = 1945

40 * 18 + 35 * p = 1945

720 + 35 * p = 1945

subtract 720 from both sides to isolate the p and its coefficient

1225 = 35 * p

divide both sides by 35 to isolate p

p = 35

Therefore, each box of potatoes weighs 35 pounds

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3 years ago