To do this we need to assign some variables
d = number of dimes
n = number of nickels.
d + n = total number of coins
we know the total number of coins to be 21 so
d + n = 21
now we need to figure out how much cash her coins are worth with nickels and dimes.
we know that nickels = 0.05 (5cents)
and that dimes = 0.10 (10 cents)
so our equation would look like this
0.05n+ 0.10d = total cash. We know that the total cash is worth is $1.70 so
0.05n+ 0.10d = 1.70
We have our system with two equations and two unknown and we can solve.
0.05n+ 0.10d = 1.70
d + n = 21
Now its actually time to do some math.
lets solve the second equation for n
n = 21-d
now plug for n into the top equation
0.05(21-d)+ 0.10d = 1.70
1.05 - 0.05d + 0.10d = 1.70
now simplify
0.05d =0.65
d = 13
now that we got the number of dimes we can plug into the second equation to get the number of nickels
13+n = 21
n = 8
we have 13 dimes and 8 nickels lets check our answer
0.05(8) + 13(0.10) = 1.70
so we go the right answer.
