Answer:
He has 12 nickels
Step-by-step explanation:
let the number of Quarters be Q and number of Nickels by N
we are given that he has 18 coins, hence the number of quarters plus the number of nickels must add up to 18, i.e:
Q + N = 18 ---------(eq 1)
We also know that quarters have a value of $0.25 and nickels a value of $0.05, hence we can deduce
monetary value of the quarters = $0.25Q
monetary value of the nickels = $0.05N
we are given we are also given that the value of all the coins equals $2.10, hence,
monetary value of the quarters + monetary value of the nickels = $2.10
0.25Q + 0.05N = 2.10 -------(eq 2)
now we have a system of 2 equations and 2 unknowns. we can solve it using your preferrred method. I'll use substitution.
from (eq 1),
Q + N = 18
Q = 18 - N ----- (eq 3)
substitute equation 3 into equation 2
0.25Q + 0.05N = 2.10
0.25(18-N) + 0.05N = 2.10
4.5 - 0.25N + 0.05N = 2.1
-0.25N + 0.05N = 2.1 - 4.5
-0.2N = -2.4
N = 12
He has 12 nickels
