Question

The hanger shown in the diagram is balanced. All cherries weigh the same, all mushrooms weigh the same, and all strawberries weigh the same. The bottom of the hanger is hidden from view. Two strings could have more weights extending below the curtain. Maybe there are more, maybe there are not!

How many grams does the exotic fruit weigh, if the weight of one cherry is 7 grams?
Assume that all parts of the hanger itself (horizontal bars and vertical strings) weigh nothing.

Answer 1

56 grams

Explanation:

See attached diagram for the hanger.

There are 6 vertical string which we label in ascending order as:

1st,2nd,...6th.

On the sixth vertical string, there are two cherries.

Since it is a balanced scale, the weight on the 5th string equals that of two cherries.

The 3rd and 4th string's weight therefore equal 4 Cherries.

Therefore:

The right hand side (3rd,4th,5th and 6th string) = 4 X 2 Cherries=8 Cherries

The 1st string carries a weight of 2 Mushrooms

By the balance rule, the second string will also weigh 2 Mushrooms.

Left Hand Side(1st and 2nd string)=2 X 2 Mushrooms =4 Mushrooms

Therefore:

The Right Hand Side=The Left Hand Side

• 8 Cherries=4 Mushrooms

Since One Cherry is 7 grams

Therefore:

4 Mushrooms =7 X 8 =56 Grams

The total weight on the left hand side is 56 grams.

Therefore, the exotic fruit weighs 56 grams.