Answer:
The possible coins are:
P = penny = $0.01
N = nickel = $0.05
D = dime = $0.10
Q = quarter = $0.25
H = half dollar = $0.50
We know that Adam has 3 coins in his pocket, and all of them are different, then the money that Adam has can be represented with (A + B + C)
Behn has 3 coins, and all of them are the same, then if his coin has a value X, he has a total of 3*X
We know that Adam has half as much money as Ben, this can be written as:
(A + B + C) = 3*X/2
The easier way to solve this, is to play with different values of X, and see if we can find the values of A, B and C.
For example, if X = $0.10
then:
(A + B + C) = $0.10*(3/2) = $0.15
We can find 3 different value of coins for this equation? No, we cant, so X = $0.10 is also discarded.
if x = $0.50 then:
(A + B + C) = (3/2)*$0.50 = $0.75
Here we could have:
A = $0.50
B = $0.25
then: A + B = $0.75
But we still have the coin C.
If we take X = $0.25 then:
(A + B + C) = (3/2)*$0.25 = $0.375
We could round the right part to $0.40
then the coins in the left part would be:
A = $0.25
B = $0.10
C = $0.05
A + B + C = $0.25 + $0.10 + $0.05 = $0.40
This is a strech, but is the only thing we can make with the given problem.