A jar of quarters and nickels contains 8.90 There are 54 coins in all How many of each are there?

Answer 1

I think the easiest way to figure this out is with a system of two equations.

let #of quarters = x ; and # of dimes = y

we have: 25*x + 5*y =890 (using cents instead of dollars eliminates decimals).

we can simplify this by dividing by 5.

so: 5*x + y = 178

we also know that the total number of coins is 54.

so: x + y = 54

we can subtract this from the first equation since the variables in both equations represent the same thing ( x = quarters and y = dimes)

5*x + y = 178 - (x + y = 54) => 4*x =124

divide by 4 to reduce this.

x = 31 (so we know that there are 31 quarters)

You can plug 31 into either equation.

31 + y = 54

y=23 (23 dimes)

or

25*31 + 5*y =890 => 775 + 5*y = 890 => 5*y =115

y =23 (23 dimes)

Finally you can verify the answer by plugging both numbers back into the original equation.

25*(31) + 5*(23) should equal 890.

In summary:

If you have two unknown variables and two equations, you can solve for both.

The question had two clear variables (# of quarters and # of dimes). It also had two clear values (total value and total number of coins). from this information it is fairly easy to identify the two equations necessary.

25*x + 5*y =890

x + y = 54