SOLUTION: There are x dimes and y nickels in bag A and y dimes and x nickels in bag B. The total value of the coins is the same for both bags. The combined number of coins in the 2 bags can

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Question 1018098: There are x dimes and y nickels in bag A and y dimes and x nickels in bag B.
The total value of the coins is the same for both bags. The combined number of coins in the 2 bags cannot be:
(A) 30 (B) 40 (C) 60 (D) 80 (E) 100
Found 2 solutions by richard1234, Theo:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
It must follow that x = y (since 10x + 5y = 10y + 5x <==> x = y). Then the combined number of coins is 2x + 2y, which can also be written as 4x (or 4y). This is a multiple of 4, so (A) 30 cannot represent the # of coins.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
since a dime is worth 10 cents and a nickel is worth 5 cents, then 10x is the value of x number of dimes and 5y is the value of y number of nickels.

you are told that there are x dimes and y nickels in the first bag and you are told that there are y dimes and x nickels in the second bag.

the value of the money in the first bag is 10x + 5y.

the value of the money in the second bag is 5x + 10y.

since the value in each bag is the same, then you get:

10x + 5y = 5x + 10y

subtract 5x from both sides of this equation and subtract 5y from both sides of this equation and you get:

10x - 5x = 10y - 5y

combine like terms to get 5x = 5y

divide both sides of the equation by 5 to get x = y.

this tells you that the number of dimes and the number of nickels in each bag has to be the same.

if the combined number of coins in the 2 bag is as shown in the selections, then divide that by 2 to see the number of coins in each bag.

so you get a possibility of 15, 20, 30, 40, or 50 coins in each bag.

since the number of dimes and the number of nickels in each bag has to be the same, then divide the total number coins in each bag by 2 to get the number of dimes which will be the same as the number of nickels.

since 15/2 is not an even number, than the number of coins in each bag can't be 15.

the rest of them can be divided evenly, so they're all good except for selection a which is not good.