CPM Homework Help : CC2 Problem 6-86

A cattle rancher gave $\frac { 1 } { 3 }$ of his land to his son and kept the remaining $\frac { 2 } { 3 }$ for himself. He kept $34$ acres of land. How much land did he have to begin with?

Hint:

Drawing a diagram may be helpful.

A line segment divided into 2 parts, labeled as follows: First section, top, 1 third, bottom, question mark. Second section, top, 2 thirds, bottom, 34 acres.

Portion given to his son. Portion kept.

Hint 2:

Try to find the amount the rancher gave to his son to find the total.

Hint 3:

You can reason that the rancher gave his son half as much as he kept. Therefore, he gave his son $17$ acres of land.

Hint 4:

You can find the total by adding the portion the rancher gave to his son to the portion he kept for himself.

More Help:

You can also solve this problem by asking yourself: Two thirds of what total amount is $34$ ?

Answer:

$51$ acres of land.