Answer to Question #197344 in Algebra for Accordance

Question

Other important numerical concepts often used in algebra are exponents and roots. We mention these two ideas in the same breath as they are each other’s inverses

  Do the following:

In 1911, two hat-makers each taught their two sons to make hats.

In 1932, each of these sons taught their two sons to make hats.

In 1953, each of these sons taught their two sons to make hats.

In 1974, each of these two sons taught their two sons to make hats.

In 1995, each of these two sons taught their two sons to make hats.

How many hat-makers were there in this family by the end of 1995?

This situation in algebra:

Answer 1

By the end of 1995, there are 126 hat makers in this family as shown below:

As at 1911, there were 2 hat makers, at the end, both trained their 2 sons meaning each had 2 sons so the product is 2x2 =4

It progresses the same way through 1995:

1911: 2+4

1932: 4x2 =8

1953: 8x2= 16

1974: 16x2= 32

1995: 32x2=64

Adding up we get 2+4+8+16+32+64 = 126 hat makers