I am having trouble setting this up.

Question

Amy decided to clean out her purse and found a total of 22 coins at the bottom in Nickels, Dimes and Quarters. The total value of the coins came to $2.50. Of the number of Nickels was triple the number of dimes, find the number of Nickels, Dimes and Quarters

Answer 1

.05n +.1d +.25q = 2.50

5n + 10d + 25q = 250

n +2d +5q = 50

n+d +q = 22

n = 3d

3d +2d +5q = 50

5d +5q = 50

d +q = 10

3d +d +q = 22

4d +q = 22 subtract d+q = 10

3d =12

d =12/3 =4 dimes

n =3d = 12 nickels

q = 22-12-4 = 6 quarters

total value = 12x.05 + 4x.10 + 6x.25 = .6 +.4 +1.5 = 2.5 = $2.50

Answer 2

Hi Ashley,

 

This is a somewhat complicated problem.  I'll help you set it up using the combination method for systems of equations.  Since you're asking for help setting it up, I expect you can handle the calculations from there. 

 

25x + 10y + 3(5y) = 250    and    x + y + 3y = 22

25x + 10y + 15y = 250      ...       x + 4y = 22

 

25x + 25y = 250

 x   +  4y  =  22

 

 25x +  25y =  250

-25x - 100y = -550

 

I expect you can take it from there.  If you ned more help, let me know.

 

BTW- This problem can also be solved by Picking Numbers, but if you can do the formulas, that's great.

 

Paul L.