Let x be the number of dimes collected and y be the number of nickels collected, then we can set the following system of equations:
[tex]\begin{gathered} 0.10x+0.05y=70.40, \\ x=5y\text{.} \end{gathered}[/tex]Substituting the second equation in the first one, and solving for y we get:
[tex]\begin{gathered} 0.10(5y)+0.05y=70.40, \\ 0.50y+0.05y=70.40, \\ 0.55y=70.40, \\ y=128. \end{gathered}[/tex]Substituting y=128 in the second equation we get:
[tex]x=5\cdot128=640.[/tex]Answer: They collected 640 dimes and 128 nickels.
