A youth orginization collected nickles and dimes for a charity drive. by the end of day one they collected 27.50

Question

A youth orginization collected nickles and dimes for a charity drive. by the end of day one they collected 27.50 if there were two times as many dimes as nickels how many of each kindw was there

Answer 1

Kate:
First step is to translate the words into mathematical equations.

1. Let x = number of dimes
2. Let y = number of nickels
3. Each nickel is worth .05.   To figure out the total value of the nickels, you simply multiply the number of nickels collected by the charity by .05.  For example if they collected two nickels, then y = 2 and the total value would be 2*0.05 =  0.10 (ten cents).
4. The organization collected $27.50.  So now we have defined the variables, we can write the first equation:
1. {EQN 1}  0.10x + 0.05y = $27.50
5. In the above equation, there are two unknowns.  So you cannot uniquely solve the problem. Hence we need one more equation
6. "There are two times as many dimes as nickles".  
1. {EQN 2} x = 2y
7. Now we have our two equations, and two unknowns.  There are several ways to solve this.  Substitution may be the easiest.  Simply substitute EQN 2 into EQN 1.
1. {EQN 3}  0.10(2y) + 0.05(y) = $27.50
2. 0.20y + 0.05y = $27.50
3. 0.25y = $27.50
4. y = $27.50/.25
5. y = 110
8. So the organization collected 110 nickels.  Can you figure out how many dimes they collected?
9. When you get your answer, be sure to doublecheck your work by plugging the values back into EQN 1.  If you have the right answer, then EQN 1 should be valid for your values of x and y.