First, let's call the number of nickels you have: nn
Then, the number of dimes you would have would be 19 - n19−n
Because the number of nickels and dimes add up to $1.10$1.10 we can write:
(n xx $0.05) + ((19 - n) * $0.10) = $1.10(n×$0.05)+((19−n)⋅$0.10)=$1.10
We can now solve for nn as follows:
$0.05n + (19 * $0.10) - (n * $0.10) = $1.10$0.05n+(19⋅$0.10)−(n⋅$0.10)=$1.10
$0.05n + $1.90 - $0.10n = $1.10$0.05n+$1.90−$0.10n=$1.10
$0.05n - $0.10n + $1.90 = $1.10$0.05n−$0.10n+$1.90=$1.10
($0.05 - $0.10)n + $1.90 = $1.10($0.05−$0.10)n+$1.90=$1.10
-$0.05n + $1.90 = $1.10−$0.05n+$1.90=$1.10
-$0.05n + $1.90 - color(red)($1.90) = $1.10 - color(red)($1.90)−$0.05n+$1.90−$1.90=$1.10−$1.90
-$0.05n + 0 = -$0.8−$0.05n+0=−$0.8
-$0.05n = -$0.8−$0.05n=−$0.8
(-$0.05n)/color(red)(-$0.05) = (-$0.8)/color(red)(-$0.05)−$0.05n−$0.05=−$0.8−$0.05
(color(red)(cancel(color(black)(-$0.05)))n)/cancel(color(red)(-$0.05)) = (-color(red)(cancel(color(black)($)))0.8)/color(red)(-color(black)(cancel(color(red)($)))0.05)
n = (-0.8)/color(red)(-0.05)
n = 16
You have 16 nickels and therefore 3 dimes:
16 xx $0.05 = $0.80
3 xx $0.10 = $0.30
$0.80 + $0.30 = $1.10
