set up an equation and solve with substitution

Question

MacKenya has 427 total coins in her piggy bank. Her coins are made up of only quarters and pennies. MacKenya took her coins to the bank and got $65.71. How many quarters,q, and pennies,p, did MacKenya have?

Answer 1

     q +     p = 427

.25q + .01p = 65.71

 

Solve the 1st equation for p to get p = 427 - q

 

Plug this in to the 2nd equation to get .25q + .01(427 - q) = 65.71

 

Multiply to get .25q + 4.27 - .01q = 65.71 

or .24q = 61.44

 

So q = 61.44 / .24 = 256 quarters

and p = 427 - 256 = 171 pennies