Question

Four weights of 1, 3, 9, and 27 pounds sit on a table along with two identical boxes. One of the boxes contains an object which weighs X pounds where X is an integer between 0 and 40. Explain how, for any such X, it is possible to place some or all of the weights in the boxes so the contents of the boxes then have the same weight. Four weights of 1, 3, 9, and 27 pounds sit on a table along with two identical boxes. One of the boxes contains an object which weighs X pounds where X is an integer between 0 and 40. Explain how, for any such X, it is possible to place some or all of the weights in the boxes so the contents of the boxes then have the same weight. @Mathematics

Answer 1

Choose the statement that correctly lists equivalent ratios.

A. 1 : 6 = 20 : 120 = 5 : 30
B. 1 : 6 = 4 : 18 = 6 : 36
C. 1 : 8 = 20 : 120 = 3 : 24
D. 1 : 8 = 3 : 32 = 5 : 48

Answer 2

To answer this you need to have a really good mental image of whats going on. Picture a balance with 2 plates, one on each side. Lets say you wanted to weigh something that is 2 pounds. You place the 3 lb weight on the left side, and the 1 lb weight on the right. that will make 2 lbs.

What about 10 lbs? thats the 9 and 1 lb weight on the left. 14 lb? thats 27lbs on the left, with 9, 3, and 1on the right. See whats going on?