Eric has 130 coins consisting of nickels and quarters. The coins combined value comes to 15.90. How many of each coin does Eric have

Question

Graphing linear equations 

Answer 1

Shara, set this up as two linear equations.

 

Equation 1: Eric has 130 coins consisting of quarters and nickels. Let Q represent the quarters and N represent the nickels, than the equation is:

 

Q + N = 130

 

Equation 2: The total value of all of the coins is 15.90. Each quarter represents .25 and each nickel represents .05, then the second equation is:

 

.25Q + .05N = 15.90

 

I prefer not to work with fractions or decimals, therefore, multiple equation 2 by 100. This gives:

 

25Q +  5N  = 1590

 

Now we can solve for Q and N:

 

    Q   +   N =   130

25Q   + 5N  = 1590

 

Multiply equation 1 by -5 and add them together:

 

   -5Q   -  5N  =  -650

   25Q  + 5N  =  1590

-------------------------

   20Q           =   940

 

Divide both sides by 20 to get the value of Q:

 

Q = 47

 

Substitute for Q in one of the original equations to get the value for N

 

Q   +  N =  130

47  +  N =  130

 

Subtract 47 from both sides to find the value of N:

 

47 - 47 + N = 130 - 47

 

N = 83

 

Check the answers by replacing Q and N is the second equation

 

.25Q + .05N + 15.90

 

.25(47) + .05(83) = 15.90

 

11.75 + 4.15 = 15.90

 

15.90 = 15.90, values check.

 

Questions?