A numismatist (coin collector) decides to divide his coin collection between his children.
The oldest gets 1/2 of the collection,
the next gets 1/4, the next gets 1/5,
and the youngest gets the remaining 49 coins.
How many coins are in the collection?
2007-12-20 01:36:28 · 15 answers · asked by Rod Mac 5 in Science & Mathematics ➔ Mathematics
Let x be the number of coins.
x = 0.5x + 0.25x + 0.2x + 49
x = 0.95x + 49
x - 0.95x = 49
0.05x = 49
x = 49/0.05 = 980
2007-12-20 01:41:03 · answer #1 · answered by ? 7 · 0⤊ 0⤋
By the time he gives 49 coins, he has already given away 1/2 + 1/4 + 1/5 = 19/20 of his collection. So 49 coins is 1/20 of the collection. The total is 20*49 = 980.
2007-12-20 01:43:15 · answer #2 · answered by Andy J 7 · 0⤊ 0⤋
The answer is not zero, as even if he devides the collection it will not cease to exist. Plus, in the question he still hasn't done this for sure, he's only decided to. So, I'm going to go with 49/(1-(1/2+1/4+1/5)) = 49*20 = 980 coins and NOT zero.
2007-12-20 01:53:47 · answer #3 · answered by iheart808 3 · 0⤊ 0⤋
x/2 + x/4 + x/5 + 49 =x
20x + 10x + 8x + 1960 = 40x
38x + 1960 = 40x
1960 = 2x
980 =x
There are 980 coins.
First child gets 980/2 = 490
Second child gets 980/4 = 245
Third child gets 980/5 = 196
490 + 245 + 196 = 931 coins
The remaining 49 coins goes to the youngest
931 + 49 = 980 coins total.
2007-12-20 01:48:23 · answer #4 · answered by james w 5 · 0⤊ 0⤋
change the fractions to the same denominator.
oldest 10/20
next 5/20
next 4/20
youngest ?
add the first 3 to get 19/20 and the youngest must be 1/20 of the collection. Now we know 1/20=49. Multiply all the others by 49 to get:
oldest 490 coins
next 245
next 196
youngest 49
add them up to check and you get 980 which is double the oldest child.
2007-12-20 01:43:50 · answer #5 · answered by David R 3 · 0⤊ 0⤋
Let the total number of coins be x
1/2x + 1/4x + 1/5x + 49 = x
0.5x + 0.25x + 0.2x + 49 = x
0.95x + 49 = x
x - 0.95x = 49
0.05x = 49
x = 49/0.05
x = 980
He has 980 coins in the collection
Oldest son gets 490 (980*1/2) coins
Next gets 245 (980*1/4) coins
Next gets 196 (980*1/5) coins
Hope that helps
Hope that helps
2007-12-20 02:21:51 · answer #6 · answered by gmat g 3 · 0⤊ 0⤋
The key to this problem is to realize if you add all of the amounts you get the whole collection.
Call x the number of coins.
x/2 + x/4 + x/5 + 49 = x
19x/20 + 49 = x
49 = x/20
x=980
There are 980 coins
The amounts received are 490, 245, 196 and 49
2007-12-20 01:42:53 · answer #7 · answered by JG 5 · 0⤊ 0⤋
Let x be the number of coins in the collection then
( 0.5 + 0.25 + 0.2 )x + 49 = x => x = 980
2007-12-20 01:45:12 · answer #8 · answered by lienad14 6 · 0⤊ 0⤋
1/2 = 10/20
1/4 = 5/20
1/5 = 4/20
= 19/20
so 49 = 1/20
therefore 20/20 (all of the collection) = 980
Although if it was a riddle and not a maths question then I'd agree with none :)
2007-12-20 01:42:01 · answer #9 · answered by SteveLaw 4 · 0⤊ 0⤋
980
2007-12-20 04:31:37 · answer #10 · answered by Anonymous · 0⤊ 0⤋
Let n = the number of coins
n - .5n - .25n - .2n = 49
.05n = 49
n = 49/.05
n = 980
Just looking at it 50% + 25% +20% = 95% so 49 is 5% of the collection.
2007-12-20 01:41:33 · answer #11 · answered by Ken 7 · 0⤊ 0⤋