Answer:
There are 5 nickles, 5 dimes, and 4 quarters.
Explanation:
Pre-Solving
We are given that someone has a collection of nickles, dimes, and quarters, and they have 14 coins that equal to $1.75.
We also know that the number of dimes is equal to the number of nickles.
We want to find the number of each of the different types of coins.
Solving
Defining the Variable
Since we know that the number of dimes is the same as the number of nickles, if there are x dimes, then there should also be x nickles.
The number of the quarters would be the total - (number of nickles + number of dimes).
Since the total is 14, and the number of dimes and nickles is both x, the number of quarters will be:
14 - (x + x), or 14-2x
Here is what we have so far:
x = dimes
x = nickles
14-2x = quarters
Equation
Remember that the coins add up to $1.75 in value.
This means that x dimes will be $0.10x in value, x nickels will be $0.05x, and 14-2x quarters will be $0.25(14-2x) in value.
We can add these up all together:
0.10x + 0.05x + 0.25(14-2x) = 1.75
Solution
We can clear the decimals by multiplying everything by 100:
10x + 5x + 25(14-2x) = 175
Multiply.
10x + 5x + 350 - 50x = 175
Combine like terms.
-35x + 350 = 175
Subtract 350 from both sides.
-35x = -175
Divide both sides by -35.
x = 5
This means that there will be 5 nickles and 5 dimes.
Remember that the number of quarters is 14-2x; we can plug 5 in for x to get 14-2(5) = 14-10=4 quarters.