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