The money from two vending machines is being collected. One machine contains 30 dollar bills and a bunch of dimes. The other machine contains 38 dollar bills and a bunch of nickels. The number of coins in both machine is equal , and the amount of money that the machines collected is also equal.
How much coins are in each machine?
1 nickel = $0.05
1 dime = $0.10
The question means:
$38 + $0.05 ∙ c = $30 + $ 0.1 ∙ c
where c = number of coins
38 + 0.05 c = 30 + 0.1 c
Try to solve this equation.
The solution is:
c = 160
Thank you!
Well, the situation seems quite balanced, so let's try to find a funny solution!
Since the amount of money collected is the same in both machines, we can convert them into the same currency. Let's go with dollars and cents, because coins always bring some added cents of humor!
Let's say the number of coins in each machine is "x." In the first machine, we have 30 dollar bills and a bunch of dimes (10 cents each), so the total value collected in the first machine is 30 + 0.10x dollars.
In the second machine, we have 38 dollar bills and a bunch of nickels (5 cents each), so the total value collected in the second machine is 38 + 0.05x dollars.
Since both machines collected the same amount, we can set up the equation:
30 + 0.10x = 38 + 0.05x
Now, let's solve this equation and find out how this funny coin saga unfolds!
Let's assume the number of coins in each machine is x.
The value of the dimes in the first machine would be 10x cents, since there are 10 cents in a dime.
The value of the nickels in the second machine would be 5x cents, since there are 5 cents in a nickel.
The value of the dollar bills in the first machine would be 30 dollars, or 3000 cents.
The value of the dollar bills in the second machine would be 38 dollars, or 3800 cents.
Since the total amount of money collected is equal, we can equate the two expressions:
10x + 3000 = 5x + 3800
Simplifying the equation, we have:
10x - 5x = 3800 - 3000
5x = 800
x = 800 / 5
x = 160
Therefore, there are 160 coins in each machine.
To find out how many coins are in each vending machine, we need to set up some equations to represent the given information. Let's assume the number of coins in each machine is 'x'.
First, let's calculate the total amount of money collected by each machine.
The first machine contains 30 dollar bills, which means it has a total value of 30 dollars. Since we know there are x coins in the first machine, and each dime is worth 10 cents, the value of the dimes is 10x cents.
Therefore, the total amount of money collected by the first machine is 30 dollars + 10x cents.
The second machine contains 38 dollar bills, which means it has a total value of 38 dollars. Since we know there are x coins in the second machine, and each nickel is worth 5 cents, the value of the nickels is 5x cents.
Therefore, the total amount of money collected by the second machine is 38 dollars + 5x cents.
According to the given information, the total amount of money collected by both machines is equal. So we can set up an equation:
30 dollars + 10x cents = 38 dollars + 5x cents
To simplify the equation, we convert dollars into cents:
3000 cents + 10x cents = 3800 cents + 5x cents
Next, we can solve for x by isolating the x term:
10x - 5x = 3800 cents - 3000 cents
5x = 800 cents
Divide both sides of the equation by 5:
x = 160
Therefore, there are 160 coins in each vending machine.