Question

Mr. harman needs to know the combined weight in pounds of three boxes he wants to mail. however, the only available scale is not accurate for weights less than 100 pounds or more than 150 pounds. so the boxes are weighed in pairs in every possible way. the results are 122 , 125 and 127 pounds. what is the combined weight in pounds of the three boxes?

(a) 160
(b) 170
(c) 187
(d) 195
(e) 354

Answer 1

To find the combined weight of the three boxes, we can assign variables to their weights and solve a system of equations. The combined weight is 187 pounds.

Therefore, the correct answer is: option c) 187.

Step-by-step explanation:

Let's assign variables to the weights of the boxes.

Let x be the weight of the first box, y be the weight of the second box, and z be the weight of the third box.

We are given the weights of the pairs of boxes:

122 = x + y, 125 = x + z, and 127 = y + z.

We can now solve these equations to find the values of x, y, and z. By adding the first two equations, we get 247 = 2x + y + z.

Subtracting the third equation from this, we get 120 = 2x. Therefore, x = 60.

Substituting this value into the first equation, we can solve for y:

122 = 60 + y, which gives y = 62.

Finally, substituting these values into the second equation, we can solve for z:

125 = 60 + z, which gives z = 65.

The combined weight of the three boxes is x + y + z

= 60 + 62 + 65

= 187 pounds.