SOLUTION: Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.4

Question 189726: Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. how many coins of each type did Sam find?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let n=# of nickels, d=# of dimes, and q=# of quarters

Since "He found six more dimes than nickels but three times as many quarters as dimes", this means that and . We'll call these equations 1 and 2.

Furthermore, because "The total value of the coins was $11.40", this means that

Note: the total value of the nickels alone is (ie the value of ONE nickel multiplied by the number of nickels). The same is applied to the dimes and quarters. These expressions are then added up to get the total value. This is probably where you're stuck.

Start with the last equation.

Multiply EVERY term by 100 to make every number a whole number

Multiply. Let's call this equation 3.

-----------------------------------------------------

So we have the equations

Equation 1:

Equation 2:

Equation 3:

You may see this as a system of equations, which looks like

=========================================================

Start with the third equation

Plug in . Notice how the variable "q" is no longer in the equation.

Multiply

Plug in . Now the variable "d" is gone.

Now we're left with a simple equation with one unknown variable.

Distribute.

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So this means that there are 7 nickels.

--------------------------------------------

Go back to the first equation

Plug in

Add

So there are 13 dimes

--------------------------------------------

Move onto the second equation

Plug in

Multiply

So there are 39 quarters.

========================================================

Answer:

So there are 7 nickels, 13 dimes and 39 quarters.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of nickels
Let = number of dimes
Let = number of quarters
given:
(1)
(2)
(3) (in cents)
---------------------------
From (1),

Now I can rewrite (3)
(3)

and from (1),

From (2),

Sam found 7 nickels, 13 dimes, and 39 quarters
check answer:
(3)

OK
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