Question

Becky has quarters dimes and nickels in her pocket the value of her money is $2.25 there are two more nickels than dimes and there are a total of 19 coins. How many dimes does becky have?​

Answer 1

Becky has 8 nickels, 6 dimes and 5 quarters in her pocket.

Explanation:

Let Number of nickels be 'n'

Let Number of dimes be 'd'.

Also Number of quarters be 'q'.

Given: there are two more nickels than dimes

hence
`n = 2+d`

Now Given:

Total Number of Coins = 19

So the equation can be framed as;

`n+d+q=19\\\\2+d+d+q=19\\\\2d+q=19-2\\\\2d+q=17 \ \ \ \ equation \ 1`

Also Given:

Total Amount in pocket = $2.25

Now we know that;

1 nickel = $0.05

1 dime = $0.1

1 quarter =$0.25

So the equation can be framed as;

`0.05n+0.1d+0.25q = 2.25\\\\0.05(2+d)+0.1d+0.25q=2.25\\\\0.1+0.05d+0.1d+0.25q=2.25\\\\0.15d+0.25q=2.25-0.1\\\\0.15d+0.25q=2.15 \ \ \ \ equation\ 2`

Now Multiplying equation 2 by 4 we get;

`4(0.15d+0.25q)=2.15*4\\\\4*0.15d+4*0.25q=8.6\\\\0.6d+q=8.6 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from equation 1 we get;

`(2d+q)-(0.6d+q)=17-8.6\\\\2d+q-0.6d-q=8.4\\\\1.4d=8.4\\\\d=(8.4)/(1.4) = 6`

Now Substituting the value of d in equation 1 we get;

`2d+q=17\\\\2*6+q=17\\\\12+q=17\\\\q=17-12\\\\q=5`

Also;

`n=2+d =2+6 =8`

Hence Becky has 8 nickels, 6 dimes and 5 quarters in her pocket.