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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 :

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. 



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