Question

Help please!

A bag of nickels and dimes contain 83 coins. If the value of the coins was $7.30, how many nickels are there? (Hint: If you call the number of nickels x, then the value of the nickels is 5x. If you call the number of dimes y, then the value of the dimes is 10y)

Answer 1

Here's another hint: if you follow the previous hint (I would), don't forget to convert $7.30 to the equivalent figure in cents!

You'll have two equations in two unknowns:

\(x\) will be the number of nickels
\(y\) will be the number of dimes
\[x+y=83\]because we have 83 coins, and they are all dimes or nickels
\[5x+10y=730\]because the value of all of the coins together is 730 cents or $7.30

Solve the system of equations for \(x\) and you'll know how many nickels there are.

Answer 2

Thank you, that helped a lot

Answer 3

I forgot to convert 7.3 to 730 and kept getting negatives.

Answer 4

You could probably this problem in your head, with a little practice. Imagine that all 83 coins were dimes (I choose dimes instead of nickels because the arithmetic is possibly a bit easier). 83 dimes is worth $8.30, which is $1 more than you want. Every dime you turn into a nickel takes 5 cents off the balance, right? We need to take $1 or 100 cents off the balance, so we convert 100/5 = 20 coins from dimes to nickels. 63 dimes and 20 nickels add up to $7.30.