Word problem

Question

Anna has $2.35 in nickels and dimes if she has thirty three coins in all find the number of nickels and dimes

Answer 1

First, read and re-read the problem until you understand it and can put it into your own words.  How's this:  "If you have 33 coins in nickels and dimes that total $2.35. how many of each coin do you have?"
 
Assign variables.
   Let n = number of nickels
   Let d = number of dimes
 
Translate:
  "Anna has $2.35 in nickels and dimes"      means    5*n + 10*d = 235
    [note: I find it easier to do all calculations in cents, then convert answer]
    [also note:   (number of coins)*(value of each coin) = (value of all coins]
 
  "she has thirty three coins in all "        means     n + d = 33
 
  "how many of each do you have?"         means      report n and d
 
Now, the easy math:
 
  Solve for either n or d (let's solve for n) in the second equation:
       n = 33 - d
  Substitute for n in the first equation:
       5*(33 - d) + 10*d = 235        [this gives and equation with only d]
        165 - 5d + 10d = 235          [distribute]
             5d = 70                      [collect terms; subtract 165 from both sides]
              d = 14                     [divide both sides by 5]
 
Now, substitute that value into the other equation.
       n = 33 - 14
        n = 19
  
Checking (very important):
  Is   5*(19) + 10*(14) = 235   ?
            95  +  140  =   235   ?
              235  = 235   ?  yes
  Is  19 + 14 = 33   ?
          33 = 33   ? yes
 
Very humble p.s.,  I often make typos and mis-reads, so I am not at all surprised that other tutors have posted different answers.  That is to be expected.  The real value is in checking the work -- just like a spelling-check program finds my typos (usually), others find my math errors and I'm thankful.  I still value the person, their knowledge, and their contribution to a better product; it is not good to belittle a person for making a mistake (we ALL make errors).  Now, here is one of my best quotes:  "With good people, a better process generally produces a better product."

See if you can find the error each other tutor made!

Answer 2

Hi Kelli, 

 

This is a system of equations problem. The first step is to set up your equations. Let D be the number of dimes we have and N be the number of Nickels. We are told that we have 33 coins total, and that their combined values are $2.35.

 

Equation 1 - Total Coins: N + D = 33 

Equation 2 - Total Value: .05N + .1D = 2.35

 

Next, take the first equation, and solve for one of the variables. In this case, we will solve for D: 

 

N + D = 33, so D = 33 - N

 

Now, substitute what we just solved for into equation 2:

 

.05N + .1D = 2.35 --> .05N + .1(33 - N) = 2.35...next distribute the .1(33 - N)....

                                =.05N + 3.3 - .1N = 2.35.....now simplify by combining the like terms:

                                = -.05N = -.95......now solve for N by dividing both sides by -.05

                                = N = 19. Since N is 19, we know that D has to be 14 to have 33 total coins. 

Answer 3

let n be number of nickels and d be number of dimes.

we have two equations from info given

1.   n+d=33

2.   n*(.05) + d*(.10) = $2.35 .... or ...      .05n + .10d = $2.35

Now solve by 2 simultaneous equations in 2 unknowns

 

Solve eq 1. for d and then sub this value for d into eq 2.

d=33-n

.05n+(33-n)*.10=$2.35 ... combine n's and simplify ...   -.05n=2.35-3.3 .... n=.95 ... there are 19 nickels !!!!

Now you finish and check your work.

Answer 4

We need to set up two equations from the information in the problem.

 

We know there are nickels and dimes.

We know there are 30 coins in total.

We know the total value of the 30 coins is $2.35.

 

From the above we can create our two equations.

 

Let n = # nickels

Let d = # dimes

 

Equation 1:

n + d = 30 

Rearranging terms we get

n = 30-d

 

Equation 2:

0.05n + 0.10d = $2.35

Notice that the coefficients are the values of nickels and dimes, respectively.

 

Let's substitute the rearranged equation 1 into equation 2

0.05(30-d) + 0.10d = 2.35

1.5 - 0.05d + 0.10d = 2.35

1.5 + 0.05d = 2.35

0.05d = 0.85

d = 17  There are 17 dimes

Since n = 30-d, so n = 30-17 = 13  There are 13 nickels