Respuesta :
Let n and d be the number of nickels and dimes, respectively. Since the total values is $5.40, we can write
[tex]0.05n+0.10d=5.40[/tex]On the other hand, since the number of nickels is two less than four times the number of dimes, we have
[tex]n=4d-2[/tex]Then, we have the following system of equations:
[tex]\begin{gathered} 0.05n+0.10d=5.40\ldots(a) \\ n=4d-2\ldots(b) \end{gathered}[/tex]Solving by substitution method.
By substituting equation (b) into (a), we have
[tex]0.05(4d-2)+0.10d=5.40[/tex]By distributing 0.05 into the parenthesis, we have
[tex]0.2d-0.1+0.10d=5.40[/tex]and by combining similar terms, we have
[tex]0.3d-0.1=5.40[/tex]then, we have
[tex]\begin{gathered} 0.3d=5.40-0.1 \\ 0.3d=5.30 \end{gathered}[/tex]By dividing both sides by 0.3, we get
[tex]\begin{gathered} d=\frac{5.30}{0.3} \\ d=17.666 \end{gathered}[/tex]