A boy has 7 more dimes than quarters. The total value of the coins is 4.90. Find the number of dimes and quarters

Question

I don't know if this problem is solvable or if I need more information.

Answer 1

There are 2 equations in 2 unknowns, so we should be able to solve the problem (that is, determine the number of dimes and the number of quarters).

 

After reading and re-reading the problem, put it into your own words.  How's this:  There is $4.90 in dimes and quarters.  There are 7 more dimes than quarters."

 

Assign variables (if possible, assign variables to the values being sought).  Let:

    D = number of dimes

    Q = number of quarters

 

Also (not included in problem) the value of a dime is 10 cents and the value of a quarter is 25 cents. So (very important) the number of cents that we have in dimes is 10D and the number of cents that we have in quarters is 25Q.  So,

    10D + 25Q = 490       (let's do everything in cents; I have trouble with decimals)

 

Translate:

  "7 more dimes than quarters"   means

    D  = 7  +  Q

 

Now, the easy math.  Let's put the value of D (from the second equation) into the first equation:

    10(7 + Q) + 25Q = 490

     70  + 10Q + 25Q = 490

          35Q = 420

              Q = 12

Substitute that value for Q into either equation (now, which one is easier??)

      D = 7 + 12

      D  = 19

 

Checking (very important):

  Is 19 really 7 more than 12 ?   yes

  Is  10(19) + 25(12) =  490  ?       (cents, remember)

       190  +  300  =  490  ?

        490   = 490   ?  yes

Answer 2

The problem is solvable with the information given.  You just need to start by creating equations to represent the information you've been given.  Let's use "d" to represent the number of dimes & "q" to represent the number of quarters.

 

The problem says "A boy has 7 more dimes than quarters." So the first equation will represent that:

 

d = q + 7

 

in other words, the number of dimes is the same as the number of quarters plus 7.

 

Next, we're told "The total value of the coins is 4.90"  and we know that the value of each dime is .10 and the value of each quarter is .25.  So we can create an equation to represent the value

 

.10d + .25q = 4.90

 

ten cents for every dime, plus twenty five cents for every quarter gives us our total of 4.90.

 

Now, we can use the first equation to replace d in the second equation, and solve for q.  We know that d = q + 7, so we can rewrite the second equation subbing "q + 7" in place of "d"

 

.10d + .25q = 4.90

 

becomes

 

.10(q + 7) + .25q = 4.90

 

Then you can solve for q.  Once you've done that, plug in the value for q into d = q + 7 & you can easily solve for d as well.