Mr. Pandy has 21 coins, all of them nickels and dimes, that are worth $1.70.
a.Write a system of equations to describe the situation
b.Solve the system
c. How many nickels and how many dimes does Mr. Pandy have?
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.
