In front of me, I have level scales. On each side, there are 3 bags. In each bag, there are some marbles. There are 150 marbles in total. Using the clues below, work out how many marbles are in each bag.
Bag 1 + Bag 2 = 56 marbles
Bag 1 + Bag 3 = 54 marbles
Bag 2 + Bag 3 = 40 marbles
Bag 4 + Bag 5 = 61 marbles
Bag 4 + Bag 6 = 37 marbles
Bag 5 + Bag 6 = 52 marbles
Answer
Bag 1 = 35 marbles
Bag 2 = 21 marbles
Bag 3 = 19 marbles
Bag 4 = 23 marbles
Bag 5 = 38 marbles
Bag 6 = 14 marbles
To work this out, since there are 150 marbles, and the scales are level, both sides of the scales must have 75 marbles. If Bag 1 + Bag 2 = 56 marbles then Bag 3 = (75-56) 19 marbles. So Bag 1 = 35 marbles and Bag 2 = 21 marbles. The same is done with Bags 4,5 and 6. Bag 4 + Bag 5 = 61 marbles. So, Bag 6 = (75-61) 14 marbles. So, Bag 4 = 23 marbles and Bag 5 = 38 marbles.