how many nickels and quarters are there when you have 71 coins which add up to $6.35

Answer 1

The total number of coins is 71. Let n = number of nickels and q = number of quarters.

n + q = 71

The total value is $6.35 = 635 cents. A nickel is 5 cents and a quarter is 25 cents. So 5n = total value of all the nickels and 25q = total value of all the quarters.

5n + 25q = 635

Now we have two equations and we can solve for one variable.

n + q = 71

n = 71 - q

5(71 - q) + 25q = 635

355 - 5q + 25q = 635

20q = 280

q = 14

We know we have 14 quarters so

n = 71 - q = 71 - 14 = 57

So we have 57 nickels and 14 quarters.