i dont get this math problem.?

Question

For the given problem, write an equation and solve it. Be sure to define the variables you use.

The coins in a piggy bank are all dimes, nickels, and quarters. There are twice as many dimes as quarters, and two more nickels than quarters. If the total value of the coins is $7.60, how many coins are in the piggy bank?

Answer 1

Hi,

They way to do this problem is to be careful in the way you set up your equations.

D= dimes
Q= Quarters
N = Nickels

Since there are twice as many dimes as quarters, you'd have to multiply the number of quarters by 2 to get it to equal the number of dimes.

2Q = D

Similarly, if there are two more nickels than quarters, you'd have to add 2 to the number of quarters to get the number of Nickels

Q + 2 = N

Now, The total value (the number of each coin times the value of the coin.) is $7.60

(0.25)Q + (0.1)D + (0.05)N = $7.60

Now you have three equations with three unknowns. Now all you have to do is isolate variables, and substitute.

Hope that helps,
Matt

Answer 2

Call the value V, the number of dimes D, nickels N and quarters Q. V = 10D + 5N + 25Q = 760. D = 2Q. N = Q + 2.

I think the easiest variable to solve in terms of is Q, since D and N are already stated in terms of it. Substitute these into the first equation: 10(2Q) + 5(Q + 2) + 25Q = 760. Multiply out the parentheses: 20Q + 5Q + 10 + 25Q = 760. Combine the Q terms: 50Q + 10 = 760. Subtract 10 from each side: 50Q = 750. Divide by 50: Q = 15.

Now, go back and find the number of dimes and nickels: D = 2Q = 2*15 = 30; N = Q + 2 = 15 + 2 = 17. There are 30 dimes, 17 nickels and 15 quarters, for a total of 62 coins in the piggy bank.

Answer 3

You're the stupidest person I know.