John had some 50cent and 10cent in a box.The number of the 50cent coins to that of the 10cent coins was in the ratio of 5:3.John took out five 50cent coins and replaced them with a number of 10cent coins of equal value.The ratio of the number of 50cent to the 10 cent coins became 1:2.Find the sum of money in the box.
2006-09-22 22:12:57 · 5 answers · asked by tocatchtheuncatchableii 3 in Science & Mathematics ➔ Mathematics
Well that's an annoying puzzle, took me a fair bit of trial and error but the answer is $14. At first there are 25 50 cent coins and 15 10 cent coins, which makes $14. Then 5 50 cent coins are taken out and 25 10 cent coins put in. So 20 50 cent coins and 40 10 cent coins remain, which also total $14.
2006-09-22 22:26:19 · answer #1 · answered by Jethro 5 · 0⤊ 0⤋
Let 50cent coins are X numbers
and 10cent coins are in Y numbers
so earlier ratio was
X:Y=5:3
In other words
X=5Y/3-------------(i)
Now, when 5 coins of 50cents removed... (that is 250cents value are removed) with similar value of 10cent coins the new number of coins in the box will be
x for 50cent coins, y for 10cent coins
x=X-5
y=Y+25
The ratio is now
(X-5):(Y+25)=1:2----------(ii)
from equation 1
replace X of eq 2 by eq 1.
[ ( 5Y / 3 ) - 5 ] / ( Y + 25 )=1:2
Solve it for Y the value is Y=15 and X = 25.
New values will be
x=20 and y=40...
so you can find the value of money before and after...
Money before replacement
=25*0.5+15*0.1=$14
After
=20*0.5+40*0.1=$14
2006-09-23 05:40:17 · answer #2 · answered by pravin K 2 · 0⤊ 0⤋
lemme see...
alright, let's take 5x as the number of 50 cent coins John has and 3x as the number of 10 cent coins he has
now, he's left with (5x - 5) 50 cent coins and (3x + 25) 10 cent coins
so 2 x (5x - 5) = 3x + 25,
or, 10x - 10 = 3x + 25
or, 7x = 35
which gives x = 5
since John took out and put back the same amount, we can just take the total sum to be (5 x 5) x 50 + (3 x 5) x 10 cents
=1250 + 150 cents
= $14
(DONE!!!)
DONE!!!
2006-09-23 05:39:30 · answer #3 · answered by Anonymous · 0⤊ 0⤋
¢50 coins number = y
¢10 coins number = Z
the total ammount of money = x
First condition
x = 50 y + 10 z
3y = 5z...........*2
2 (y - 5) = (z +25 )
2y -10 = z +25
2y -z =35 ...............*3
_______________________
6y - 10 z = 0
6y - 3 z = 105
________________
7z = 105
z = 15
y = 25
then
x = 25 * 50 + 15 *10 =
1250 + 150 = ¢1400
$14
2006-09-23 05:36:32 · answer #4 · answered by M. Abuhelwa 5 · 0⤊ 0⤋
can i have some money?
2006-09-23 05:27:38 · answer #5 · answered by Anonymous · 0⤊ 1⤋