the value of the coin times the number of coins summed up equals the total value
so
\(0.05n + 0.10d = 5.10\)
then they give us that
"you have 3 more dimes than nickels"
so
\(d = n + 3\)
or
\(n = d - 3\)
we plug this into our first equation and get
\(0.05(d - 3) + 0.10d = 5.10\)
distribute the 0.05
\(0.05d - 0.15 + 0.10d = 5.10\)
add like terms
\(0.15d - 0.15 = 5.10\)
add 0.15 to both sides
\(0.15d = 5.25\)
divide both sides by 0.15
\(d = /frac{5.25}{0.15} = 35\)
therefore your answer is there are 35 dimes
