Question

You have 30 coins worth $2.05 in nickels and dimes. What's in your wallet? Create and solve of equations to find how many dimes and how many nickels you have.WRITE 2 EQUATIONSAND I WILL DO THE WORKALL I NEED HELP WITH IS THE EQUATION BUT I KNOW HOW TO SOLVE

Answer 1

Number of nickels = 19

Number of dimes = 11

Explanation:

Given:

Total number of coins =30

Total worth of coins = $2.05

To find the number of nickels and dimes.

Solution:

Let the number of nickels be =
`n`

Let the number of dimes =
`d`

The sum of the coins will be =
`n+d`

The sum equation can be given as :

`n+d=30`.............A

Values of 1 nickel = $0.05

So, value of
`n` nickels in dollars =
`0.05n`

Value of 1 dime = $0.10

So, value of
`d` dimes in dollars =
`0.1d`

The total value of
`n` nickels and
`d` dimes in dollars will be =
`0.05n+0.1d`

Thus, the value equation can be given as:

`0.05n+0.1d=2.05`..............B

So, the system of equations are:

`n+d=30`.............A

`0.05n+0.1d=2.05`..............B

Multiplying equation B with -10.

(
`0.05n+0.1d=2.05`)
`(* -10)`

`-0.5n-1d=-20.5`

Now, adding to equation A.

`n+d=30`

`-0.5n-1d=-20.5`

-----------------------------

`0.5n=9.5`

Dividing both sides by 0.5.

`(0.5n)/(0.5)=(9.5)/(0.5)`

∴
`n=19`

∴
`d=30-19=11`

Thus, number of nickels = 19

Number of dimes = 11