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Question

A collection of nickels, dimes, and quarters consist of 12 coins with a total of $1.25. If the number of dimes is equal to the number of nickels, find the number of each type of coins.

Answer 1

There are a number of coins nickles, dimes and quarters.   This constitutes three unknowns.   If we can establish three independent linear equations, then we can solve for n, d, and q, the number of nickels dimes and quarters respectively.

 

Since total value is $1.25  we can write (0.05)n + (0.10)d + (0.25)q = 1.25

Since there are twelve coins we write                              n + d + q = 12

Since the number dimes equal the number of nickels        n   = d

 

 

You can solve those three equations in a variety of ways using methods appropriate to what you have been taught.

Let's use n = d in the first two equations to eliminate the variable n

 

0.05d + 0.10d + 0.25q  =  0.15d + 0.25q  = 1.25

d + d + q =                      2d      + q        = 12

 

No let's use elimination to remove variable d.    Multiply the first equation by 2 and the bottom equation by 0.15 then subtract 

 

2 * (0.15d + 0.25q = 1.25)    =>  0.12d + 0.50q    = 2.50

0.15 *( 2d + q = 12)                    0.30d  +0.15q   = 1.80

 

subtracting yields                                    0.35q = .7    q = 2

 

putting two back into the first equation   0.15*d + 0.25(2) = 1.25   0.15d = 0.75   d = 5

since there are 5 dimes there are also 5 nickles.   

Answer 2

In this problem you would need to set up 2 equations with the information given to you. First let x equal the number of nickels, also, you know that the number of dimes is the exact same to x will also represent dimes. Let y represent your quarters.

Your first equation would be set up like this:

x+x+y=12

 

because we know you have a total of 12 coins.

The second equation uses the total amount of money you have and the amount each coin is worth. It would look like this:

0.05x+0.10x.0.25y=1.25

 

Now that we have these 2 equations we can use substitution to solve them both

 

The first equation simplifies to this:

x+x+y=12

2x+y=12

 

Rearrange the equation so only one variable is equal to everything else. Let's make it y since that's the easiest.

 

y=12-2x

Now substitute that into the other equation where you have a y variable.

 

0.05x+0.10x+0.25(12-2x)=1.25   Simplify

 

0.15x+3-0.5x=1.25

 

3-0.35x=1.25

 

-0.35x=-1.75

 

x=5

 

Since x represented the number of nickels and dimes you have only the quarters left to fine. Plug 5 back into the first equation and simplify to fine y

 

5+5+y=12

10+y=12

y=2

 

So you have 5 nickels, 5 dimes, and 2 quarters. Plug those into your second equation to check you work and make sure it adds up to the correct amount.