A sum of money was shared among Amos, Benny and Cathy. Amos received 1/4 of the sum. Benny received 2/5 of the remainder and Cathy received the rest.

As a result, Cathy received $150 more than Benny.

(a) What is the amount received by
Amos?
(b) Find the sum of money?

Let s = sum

(1/4)s + (2/5)(3/4)s + (2/5)(3/4)s + 150 = s

(1/4)s + (3/5) s + 150 = s

(5/20 + 12/20) s +150 = s

(17/20)s + 150 = s

(3/20) s = 150

s = 50*20 = 1000
Amos get 1/4 of that or 250

To find the answers to this problem, we can break it down step by step.

Let's assume the sum of money shared among Amos, Benny, and Cathy is represented by S.

(a) Amount received by Amos:
Amos received 1/4 of the sum, which can be expressed as (1/4)S.

(b) To find the sum of money:
First, let's calculate the money that is remaining after Amos received his share. This is represented by (S - (1/4)S).

Benny received 2/5 of the remainder, so Benny's share is (2/5)(S - (1/4)S).

Cathy received the rest of the money, which is the remaining amount after both Amos and Benny received their shares. This can be expressed as:

(S - (1/4)S) - (2/5)(S - (1/4)S)

From the problem, we know that Cathy received $150 more than Benny. So we have the equation:

((S - (1/4)S) - (2/5)(S - (1/4)S)) - ((2/5)(S - (1/4)S) + $150) = ((2/5)(S - (1/4)S))

Simplifying the equation further, we get:

(S - (1/4)S) - (2/5)(S - (1/4)S) - (2/5)(S - (1/4)S) - $150 = (2/5)(S - (1/4)S)

We can now solve for S by isolating it on one side of the equation:

(S - (1/4)S) - (2/5)(S - (1/4)S) - (2/5)(S - (1/4)S) - $150 = (2/5)(S - (1/4)S)

Combining like terms, we get:

(1 - (1/4) - (2/5) - (2/5))S + $150 = (2/5)(S - (1/4)S)

Simplifying further:

(11/20)S + $150 = (2/5)(5/4)S

Multiplying both sides by 20 to remove the fraction:

11S + $3000 = 16S

Now, isolate S by moving 11S to the other side:

$3000 = 16S - 11S

$3000 = 5S

Finally, divide both sides by 5:

S = $600

Therefore, the sum of money shared among Amos, Benny, and Cathy is $600.

To find the amount received by Amos, substitute the value of S into the equation for Amos' share:

Amos' share = (1/4)S = (1/4)($600) = $150

Therefore, Amos received $150.