coins in a jar

Question

Kevin and Randy Muise have a jar containing
62
?coins, all of which are either quarters or nickels. The total value of the coins in the jar is
?$11.30
How many of each type of coin do they? have?

Answer 1

Hi Jessica,

We know:

Q+N=62 and Q(0.25)+N(0.05)=11.30

 

We can rearrange the first equation to solve for either Q or N (let's solve for Q)

Q=62-N

 

Now we can plug 62-N into the second equation as a substitute for Q

(62-N)(0.25)+N(0.05)=11.30

 

Solve for N to find how many nickels they have, and then plug it back into the rearranged first equation to solve for Q (the number of quarters they have)

Answer 2

 

Let n = number of nickels

Let q = number of quarters

 

since the total number of coins is 62,

 

    n + q = 62

 

since the amount of money is $11.30,

 

    .05n + .25q = 11.30

 

solving for q in the first equation, we have q = 62 - n

 

substituting that into the second equation, we have

 

     .05n + .25(62 - n) = 11.30

     .05n + 15.5 - .25n = 11.30

     -.20n = 11.30 - 15.5

     -.20n = -4.20

     n = 21

 

since n + q = 62,

 

      q = 62 - 21 = 41

 

Thus, there are 41 quarters ($10.25) and 21 nickels ($1.05)