### Brain Teasers

# Bags, Marbles, and Scales

Math
Math brain teasers require computations to solve.

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

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 marblesBag 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.

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