Answer: The required number of quarters is 12 and that of dimes is 8.
Step-by-step explanation: Given that Brandon has a cup of quarters and dimes with a total value of $3.80 . The number of quarters is 4 less than twice the number of dimes.
We are to find the number of quarters and dimes that Brandon has.
We know that
1 quarter = 0.25 dollar and 1 dime = 0.10 dollar.
Let q and d represents the number of quarters and dimes respectively that Brandon has.
According to the given information, we have
[tex]0.25q+0.10d=3.80\\\\\Rightarrow 25q+10d=380\\\\\Rightarrow 5q+2d=76~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]q=2d-4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of q from equation (ii) in equation (i), we get
[tex]5(2d-4)+2d=76\\\\\Rightarrow 10d-20+2d=76\\\\\Rightarrow 12d=96\\\\\Rightarrow d=\dfrac{96}{12}\\\\\Rightarrow d=8.[/tex]
And, from equation (ii), we get
[tex]q=2\times8-4=16-4=12.[/tex]
Thus, the required number of quarters is 12 and that of dimes is 8.
