Question

Jordan has only dimes and nickels in his piggy bank. He has a total of 77 coins. The value of the coins is $6.95 . Write and solve a system that can be used to determine how many dimes and how many nickels he has .

Answer 1

From the text we have the following system:

`D+N=77`

&

`0.1D+0.05N=6.95`

[We know that 1 dime is 0.1 USD and 1 nickel is 0.05 USD]. Now we solve as follows:

*First: We solve the first expression for D or N, that is:

`D=77-N`

*Second: We replace the value of D in the second expression and solve for N:

`0.1(77-N)+0.05N=6.95\Rightarrow7.7-0.1N+0.05N=6.95`
`\Rightarrow7.7-0.05N=6.95\Rightarrow-0.05N=-0.75`
`\Rightarrow N=15`

*Third: Now that we know the number of nickels, we replace them in the first equation and solve for D:

`D+15=77\Rightarrow D=62`

From this, we have that Jordan has 62 dimes and 15 nickels in his piggy bank.