4th Question :
Four children ,Alice ,Bernard and Cassie and Dominic shared a
sum of money .Alice received twice the total amount of money
received by Bernard ,Cassie and Dominic .Bernard received [2/3] the
total money Cassie and Dominic received .
Dominic received 5 times as much as Cassie .
(a) What fraction of the total amount of money was Cassie’s
Money ?
(b) Alice used half her money ,or $50 ,to buy a watch .Bernard
also gave half of his money to Cassie .How much money did Cassie
have in the end .
+++++++++++++++++++++++++++++++++++
lets use A B C D to denote the amount each
kid receive.
we know,
A = 2 (B+C+D)
B = 2/3 (C+D)
D = 5C
So, substitution:
B= 2/3(C+5C)
B= 4C
Substitute this, together with D=5C into the first equation, you
get:
A=2(4C+C+5C)
A=20C
expanding,
since we are looking at fraction, the total amount must add up
to 1
so,
20C+4C+C+5C = 30C
30C = 1
therefore, Cassie receives only 1/30 of the share
part 2
since 1/2 A = 50, A = 100
we know, A= 20C, therefore C = 5
and B gives half to C, B = 4C = 20, gives half, meaning, C
receives 10
add to the 5 +10 = 15.
