Question

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?

Answer 1

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.