swerve wrote:After his death, a farmer left all of his land to his three children. and 25% more than Stephen. If James received 3,600 acres, how many acres did Stephen get?

A. 2,400
B. 3,456
C. 3,600
D. 3,750
E. 4,320

Alfred received 20% more acres of land than James.
If J=100, then A=120.
The following ratio is implied:
A/J = 120/100 = 6/5.

Alfred received 25% more acres 25% than Stephen.
If S=100, then A=125.
The following ratio is implied:
S/A = 100/125 = 4/5.

If James received 3,600 acres, how many acres did Stephen get?
S/J = S/A * A/J.
In the equation above, the values in red CANCEL OUT.
Substituting S/A = 4/5 and A/J = 6/5 into the equation above, we get:
S/J = (4/5) * (6/5) = 24/25.

Implication of the ratio in blue:
For every 25 acres that J receives, S receives 24 acres.
Thus, the number of acres for S must be just a bit less than the number of acres for J.
Since J=3600, the correct answer must be just a bit less than 3600.

The correct answer is B.

swerve wrote:After his death, a farmer left all of his land to his three children. Alfred received 20% more acres of land than James and 25% more than Stephen. If James received 3,600 acres, how many acres did Stephen get?

A. 2,400
B. 3,456
C. 3,600
D. 3,750
E. 4,320

Since James received 3,600 acres of land and Alfred received 20% more than than James, Alfred received 1.2 x 3,600 = 4,320 acres of land.

Since Alfred received 25% more land than Stephen, we can let the number of acres of land Stephen received be n and create the following equation:

1.25n = 4,320

n = 3,456

Alternate Solution:

We are given that Alfred received 20% more than than James and 25% more than Stephen. Thus, Stephen received the least amount of land. However, the amount of land Stephen received would be just "somewhat" less than what James received. Since James received 3,600 acres of land, Stephen must have received 3,456 acres of land since that's the only number that is "somewhat" less than 3,600.

Answer: B