A collection of 35 coins contains nickels and dimes. Find the number of dimes given that the total sees value of the coins is $2.55

Question

I don't know how to do the work

Answer 1

Let n = number of nickels and d = number of dimes

 

n + d = 35                    (The number of nickels and the number of dimes total in 35 coins)

 

0.05n + 0.1d = 2.55      (Multiply number of nickels & dimes by their respective values to get the total dollar amount)

 

This is a system of equations. We are going to have to add/subtract one from the other, so we will need to multiply the first equation by -0.05 in order to cancel out the nickels when we combine these equations.

 

-0.05(n + d) = -0.05(35)

-0.05n -0.05d = -1.75

 

Now we can add the 2 equations:

 

 0.05n + 0.1d = 2.55

-0.05n - 0.05d = -1.75

                                  

0n + 0.05d = 0.8

 

0.05d = 0.8                    (Divide by 0.05 on both sides)

d = 16

 

So the number of dimes is 16.

Answer 2

Let x=nickles and y=dimes and set up a system of equations in 2 variables:

 

x + y = 35

 

5x + 10y = 255

 

And solve via elimination or substitution