A collection of nickels and quarters has a total value of $6.40. If there are forty coins in the collection, how many are there of each kind?

There are 18 nickels and 22 quarters

Step-by-step explanation:

Notice that nickels are worth 5 cents and quarters are worth 25 cents.

We will develop two equations using the given information. the number of nickels will be represented by x and the number of quarters will be represented by y.

5 cent is the same as 0.05

and 25 cents is the same as 0.25

0.05x + 0.25y = 6.40  This equal can be used to model the first statement.

There are forty collection which means a combination of nickels and quarters has to equal 40 and that can also be represented by the equation x +y=40

0.05x + 0.25y = 6.40

x + y = 40  

Using both equations, we can solve for x and y using the elimination method.

To eliminated the x variable multiply the down equation by -0.05.

-0.05(x+y) = -0.05(40)   Multiply to get the new equation ,

-0.05x - 0.05y = -2    

Combine the first equation with the new equation.

0.05x + 0.25y = 6.40

-0.05x - 0.05y = -2     Add both equations

             0.2y = 4.4

            y= 22

This means that there are 22 quarters  and to find the number of nickels we will subtract 22 from 40.  

40 -22 = 18  

There are 18 nickels

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step-by-step explanation: