How many of each coin are there?

Question

a box contains 35 coins in quarters and nickels worth $3.15

Answer 1

Let x be the number of quarters.

 

Let y be the number of nickels.

 

The number of quarters x plus the number nickels y will equal 35 coins total. That's our first equation.

 

x + y = 35

 

This equation expresses the quantity of coins

 

 

We can form another equation that expresses the monetary value of the coins.

 

Each quarter x is worth 25 cents or $0.25. 

Each nickel y is worth 5 cents or $0.05

The sum of the monetary values of the quarters and nickels is total monetary value of our collection of coins, which is $3.15 

That's our second equation.

 

0.25x + 0.05y = 3.14

 

 

So our system of equations is 

 

x + y = 35

0.25x + 0.05y = 3.14

 

 

Solving for x in the first equation, we get

 

x = 35 - y

 

We can plug this value for x into the second equation and solve for y.

 

0.25(35 - y) + 0.05y = 3.14

 

8.75 - 0.25y + 0.05y = 3.14

 

8.75 - 0.20y = 3.14

 

-0.20y = 3.14 - 8.75

 

y = (3.14 - 8.75)/-0.20

 

   = 28

 

We can plug this value for y into the first equation to solve for x.

 

x + (28) = 35

 

x = 35 - 28

 

   = 7

 

So the number of quarters x is 7.

and the number of nickels y is 28.

 

We can plug both values into both equations, and if the statements are true, then the values are correct.

 

7 + 28 = 35

       35 = 35           True!

 

 

0.25(7) + 0.05(28) = 3.14

 

1.75 + 1.4 = 3.14

          3.14 = 3.14   True!