coin question

Question

Kevin and Randy Muise have a jar containing 61
?coins, all of which are either quarters or nickels. The total value of the coins in the jar is ?$ 9.05.
How many of each type of coin do they? have?

Answer 1

Shawn,

 

We solve this using a system of linear equations.

 

N = # nickels

Q = # quarters

 

N + Q = 61

.05N + .25Q - 9.05

 

We can use substitution here.

Since N + Q = 61, then Q = 61-N

 

Substituting this in the 2nd equation

.05N + .25(61-N) = 9.05

.05N + 15.25 - .25N = 9.05

15.25 - .2N = 9.05

-.2N = -6.2

N = 31

and therefore Q = 30

 

There are 31 nickels and 30 quarters

Answer 2

We can solve this problem using a system of equations, when we make n the number of nickels and q the number of quarters. First we have:

n+q=61

because the number of nickels plus the number of quarters is 61. Next we have:

.25q+.05n=9.05

because we know every quarter is worth .25 and every nickel is worth .05 and they add to equal 9.05

If we rearrange the first equation by subtracting n on both sides we can make it:

q=61-n

And now we can plug 61-n in for q in the second equation, giving us:

.25(61-n)+.05n=9.05

We distribute the .25 to give us

15.25-.25n+.05n=9.05

Now we can combine like terms and subtract the 15.25 on both sides to give us

-.2n=-6.2

And diving the -.2n on both sides leaves us with the number of nickels

n=31

Simply plug that value into any of the equations containing an n and a q (easiest is q=61-n) and solve for q to find

q=30

 

So the final answer would be 31 nickels and 30 quarters

Answer 3

Let n be the number of nickels and q the number of quarters.

 

(1) n + q = 61

 

(2) 5n + 25q = 905

     n + 5q = 181

 

From (1), n = 61 - q

 

Substitute this value into (2)

 

61 - q + 5q = 181

4q = 120

q = 30

 

Then n = 61 - 30 = 31

 

They have 31 nickels and 30 quarters.