when i try to put 5 coins into each cup, i end up with 2 coins in the last cup. when i put 3 coins into eachcup, i had 9 coins laft over. there are less than ten cup. how may coins do i have, and with how many cups?
2006-07-25 12:35:41 · 6 answers · asked by Mona P 1 in Science & Mathematics ➔ Mathematics
n = coins
c = cups
Equation for 5 coins (c-1 cups* filled with 5 + 2 extra):
5(c-1) + 2 = n
5c - 5 + 2 = n
5c - 3 = n
Equation for 3 coins (c cups filled with 3 + 9 extra):
3c + 9 = n
Subtracting #2 from #1:
2c -12 = 0
2c = 12
c = 6
Plugging c = 6 back into #1:
5c - 3 = n
5(6) - 3 = n
n = 30 - 3
n = 27
6 cups
27 coins
Double-checking:
27 coins would fill up 5* cups with 5 coins, with 2 in the last cup
27 coins would fill up 6 cups with 3 coins, with 9 left over.
*The tricky part is noticing the wording says that all but the last cup are filled (c-1), while the second arrangement has all cups (c) filled.
So the answer is:
6 cups, 27 coins
2006-07-25 12:44:15 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
Cool problem. You need to have symbols for what you don't know. Let "X" stand for the number of cups, and let "Y" stand for the number of coins. You have two unknowns, and two facts, so this might just work out.
Translate the first fact into symbols:
5 coins in each cup but the last means 5*(X-1)
so the first fact translates into the equation
5*(X-1)+2=Y
Notice the +2 is for the last cup, and all of the coins are in cups, so the total must be Y.
You probably can figure out how to translate the second fact into symbols on your own. If you can't, come back to the board for more help.
2006-07-25 12:44:57 · answer #2 · answered by Benjamin N 4 · 0⤊ 0⤋
You could have 6 cups and 27 coins... I set it up as the variable x representing the number of cups, so we got 5(x-1) + 2 to represent 5 coins in each cup but one and 2 in the last cup. On the other side, you would have 3x + 9 to represent 3 in each cup with 9 coins left over.
Now set them equal to each other and solve to get x = 6, so 6 cups and hence, 3*6+9 coins, or 27 coins... :-)
2006-07-25 12:42:57 · answer #3 · answered by Chris 2 · 0⤊ 0⤋
Let's see... 5(x-1)+2 = 3x+9, where x is the amount of cups.
So 5x-3 = 3x+9. 2x=12, so that means x must equal 6. So you have 6 cups, and 27 coins.
2006-07-25 13:04:45 · answer #4 · answered by Anonymous · 0⤊ 0⤋
4 cups, 22 coins.
2006-07-25 12:39:55 · answer #5 · answered by Anonymous · 0⤊ 0⤋
42-9 cups
36-9 cups
2006-07-25 12:49:47 · answer #6 · answered by Anonymous · 0⤊ 0⤋