Question 1024516: Melvin and Philip have a collection of coins from Australia and New Zealand. Melvin and Philip have equal number of coins from Australia. 4/5 of Philip's coins are from Australia and 1/13 of Melvin's coins are from New Zealand. Given that both of them have a total of 12 coins from New Zealand, how many coins does each of them have ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let m = the coins that melvin has.
let p = the coins that philip has.
4/5 of philip's coins are from australia.
this means that 1/5 of philip's coins are from new zealand.
1/13 of melvin's coins are from new zealand.
this means that 12/13 of melvin's coins are from australia.
you know that the total coins from new zealand are 12 and that they are split equally between melvin and philip.
this means that melvin has 6 and philip has 6 coins from new zealand.
since 1/5 of philip's coins come from new zealand, then you get 1/5 * p = 6.
solve for p to get p = 30.
since 1/13 of melvin's coins are from new zealand, then you get 1/13 * m = 6.
solve for m to get m = 78.
philip has 30 coins total.
melvin has 78 coins total.
both of them have 108 coins total.
the breakdown is as follows:
melvin has 6 coins from new zealand and 72 coins from austraila.
1/13 * 78 = 6
12/13 * 78 = 72
philip has 6 coins from new zealand and 24 coins from australia.
1/5 * 30 = 6
4/5 * 30 = 24
if you were to draw a 2 dimensional table, it would look like this:
m p t
z 6 6 12
a 72 24 96
t 78 30 108
m is the number of coins that melvin has.
p is the number of coins that philip has.
z is the number of coins from new zealand.
a is the number of coins from australia.
t column is the total number of australian coins and the total number of new zealand coins.
t row on the bottom is the total number of coins that melvin has and the total number of coins that philip has.
|
|
|
