On monday, Tanya counted the number of 10-cent coins, 20-cent coins and 50-cent coins in her piggy bank. The number of 10-cent coins was 24 more than the number of 50-cent coins. On tuesday, Tanya spent 3 over
5 of the 10-cent coins, 1 over 4 of the 20-cent coins and 18 50-cent coins. Tanya then found that she had an equal number of 10-cent coins and 20-cent coins. The number of 50-cent coin now formed 40% of all the coins she had left.
(a)Tanya had how many 10-cent coins at first?
This one is really confusing is it not :)
Let the number of tens be X, the number of twenties be Y and the number of fifties be Z
Z+24=X
X-24=Z
-----
now after her spending spree this is what what she has left
(2/5)X+(3/4)y+(Z-18) coins
and
(2/5)X=(3/4)Y
so Y = 0.4X/0.75 = (8/15)X and from before X-24=Z
also
0.4((2/5)X+(3/4)y+(Z-18) )=Z-18
The first thing we want is X so I will get all this in terms of X and solve and hopefully the answer is a whole number. :)
0.4((2*(2/5)X+(X-24-18))=X-24-18
0.4((0.8X+(X-42))=X-42
0.4(1.8X-42)=X-42
0.4*1.8X - 0.4*42=X-42
0.72X - 16.8 =X - 42
-16.8+42 =X - 0.72X
25.2=0.28X
X=90
so there was originally 90 ten cent peices
(b)How much money did Tanya spent in all?
X=90
Y=(8/15)X = 8/15*90 = 48
She spent (3/5)*X = (3/5)*90 = 54 ten cent coins = $5.40
She spent (1/4)*Y = 0.25*48 = 12 twenty cent coins = $2.40
She spent 18 fifty cent coins = $9
Total spent = 5.40+2.40+9= $16.80
I fixed this after CPhill told me, by Private message, of a careless error. Thanks Chris 
I only just realized that he has posted a proper answer underneath then whited it out.
You don't need to do that Chris - I shall unwhite it. It is a good answer :)
)
