Respuesta :
Answer:
Becky has 8 nickels, 6 dimes and 5 quarters in her pocket.
Step-by-step 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 [tex]n = 2+d[/tex]
Now Given:
Total Number of Coins = 19
So the equation can be framed as;
[tex]n+d+q=19\\\\2+d+d+q=19\\\\2d+q=19-2\\\\2d+q=17 \ \ \ \ equation \ 1[/tex]
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;
[tex]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[/tex]
Now Multiplying equation 2 by 4 we get;
[tex]4(0.15d+0.25q)=2.15\times4\\\\4\times0.15d+4\times0.25q=8.6\\\\0.6d+q=8.6 \ \ \ \ equation \ 3[/tex]
Now Subtracting equation 3 from equation 1 we get;
[tex](2d+q)-(0.6d+q)=17-8.6\\\\2d+q-0.6d-q=8.4\\\\1.4d=8.4\\\\d=\frac{8.4}{1.4} = 6[/tex]
Now Substituting the value of d in equation 1 we get;
[tex]2d+q=17\\\\2\times6+q=17\\\\12+q=17\\\\q=17-12\\\\q=5[/tex]
Also;
[tex]n=2+d =2+6 =8[/tex]
Hence Becky has 8 nickels, 6 dimes and 5 quarters in her pocket.
