5 of what remained to the next youngest, and what remained to the eldest. How mu...

Questions

August 2021 1 67 Report

A farmer has 3 daughters and 7 1/4 hectares of land. He gave 2/5 of it to the youngest daughter, 3/5 of what remained to the next youngest, and what remained to the eldest. How much land did each daughter receive?
Illustration:

Given:
Required:
Solution:

Answers & Comments

hanzysomera88

Problem:

A farmer have 3 daughters and 7 ¼ hectares of land. He gave ⅖ of it to the youngest daughter, ⅗ of what remained to the next youngest, and what remained to the eldest. How much land did each daughter receive?

Given:

A farmer has 3 daughters and 7 ¼ hectares of land. He gave ⅖ of it to the youngest daughter, ⅗ of what remained to the next youngest, and what remained to the eldest.

Required:

How much land did each daughter receive.

Solution:

Youngest daughter:

$7 \: \frac{1}{4} \times \frac{2}{5} = x \\ x = \frac{29}{4} \times \frac{2}{5} \\ x = \frac{29}{2} \times \frac{1}{5} \\ x = \frac{29}{10} \\ x = 2 \: \frac{9}{10}$

Next youngest:

$(7 \: \frac{1}{4} - 2 \: \frac{9}{10} ) \frac{3}{5} = y \\ y = (7 \: \frac{5}{20} - 2 \: \frac{18}{20} ) \frac{3}{5} \\ y = (6 \: \frac{25}{20} - 2 \: \frac{18}{20} ) \frac{3}{5} \\ y = 4 \: \frac{7}{20} \times \frac{3}{5} \\ y = \frac{87}{20} \times \frac{3}{5} \\ y = \frac{261}{100} \\ y = 2 \: \frac{61}{100}$

Eldest:

$(7 \: \frac{1}{4} - 2 \: \frac{9}{10} ) - 2 \: \frac{61}{100} = z \\ z = (7 \: \frac{5}{20} - 2 \: \frac{18}{20} ) - 2 \: \frac{61}{100} \\ z = (6 \: \frac{25}{20} - 2 \: \frac{18}{20} ) - 2 \: \frac{61}{100} \\ z = 4 \: \frac{7}{20} - 2 \: \frac{61}{100} \\ z = 4 \: \frac{35}{100} - 2 \: \frac{61}{100} \\ z = 3 \: \frac{135}{100} - 2 \: \frac{61}{100} \\ z = 1 \: \frac{74}{100} \\ z = 1 \: \frac{37}{50}$

Checking:

$2 \: \frac{9}{10} + 2 \: \frac{61}{100} + 1 \: \frac{37}{50} = n \\ n = 2 \: \frac{90}{100} + 2 \: \frac{61}{100} + 1 \: \frac{74}{100} \\ n = 5 \: \frac{225}{100} \\ n = 6 \: \frac{125}{100} \\ n = 7 \: \frac{25}{100} \\ n = 7 \: \frac{1}{4}$