solving using systems of equations

Question

eric has 130 coins consisting of nickles and quarters. The coins combined value comes to $15.90. find out how many of each coin does eric have? solve this using systems of equations

Answer 1

There are two parts to this equation.

 

The number of total coins:

x + y = 130

 

The combined value of nickels and quarters. Multiply the variables by the cash value of the coins.

0.05x + 0.25y = 15.90

 

From here find a value for x or y using one of the two equations (ie x = 130 -y) and substitute and solve for a variable. 

 

.05(130-y) + .25y = 15.90

 

another way is to normalize your values and subtract equations. In this case we will turn the value of .25y into -1y by multiplying everything by -4 for instance. This will give us a negative y value (-1y) that we can use to add to the value in the first equation. By cancelling out one variable (-y + y = 0) we can solve for x.

 

-4(.05x + .25y) = -4(15.90)

 

 

   -.2x - y = -63.6 (this will eliminate the value of y to solve for x)

+    x + y = 130

______________

 

add the equations to solve for one variable, then solve the other. Plug your answers into both formulas to check them.

 

You can search for more examples of solving systems of equations if you need to see examples in action (I'm not going to flat out give you the answers).

 

 

Regards,
Chris

 

Answer 2

Let # of nickels = x

Let # of quarters = y

 

 

Set up equations.

 

x + y = 130                        eq1

0.05x + 0.25y = 15.90         eq2

 

 

Substitute eq1 into eq2.

 

0.05x + 0.25(130 - x) = 15.90

0.05x + 32.50 - 0.25x = 15.90

-0.20x = -16.60

        x = 83

 

Substitute this value into eq1.

 

y = 130 - x

y = 130 - 83

y = 47

 

There are 83 nickels and 47 quarters.