Question

Diana has been saving nickels and dimes. She opened up her piggy bank and determined that it contained 48 coins worth $4.50. Determine how many nickels and dimes were in the piggy bank.

Answer 1

Answer:

6 Nickels

42 Dimes

Step-by-step explanation:

There are 48 coins in total (nickels and dimes). Let the number of nickels be "n" and the number of dimes be "d". So we can write:

n + d = 48

or

n = 48 - d

In dollars, we know nickels are worth 0.05 and dimes are worth 0.10. In total there is $4.50, so we can write:

0.05n + 0.10d = 4.50

Now replacing first equation [n = 48 - d] into 2nd, we get and equation in "d" and solve for d first:

$0.05n + 0.10d = 4.50\\0.05(48-d) + 0.10d = 4.50\\2.4-0.05d+0.10d=4.50\\0.05d=4.50-2.4\\0.05d=2.1\\d=\frac{2.1}{0.05}=42$

So, there are 42 dimes.

We know from before, n = 48 - d, so

n = 48 - 42 = 6

There are 6 nickels