Question 786864
<pre>
The other tutor used three unknowns.  Here is the way to do it 
with only one unknown.
</pre>
SOS. I am not good at word problems. You have 10 fewer quarters than dimes and 5 fewer nickels than quarters. The total value of the coins is $4.75. How many quarters nickels and dimes do you have?

>>...10 fewer quarters than dimes...<<
<pre>
We know from reading that, that there are more dimes and less quarters, and
that their numbers differ by 10.

So we can say that either of two ways: 
"smaller = larger minus 10", or
"larger = smaller plus 10".

{{{(matrix(5,1,

NUMBER,OF,QUARTERS,"(smaller","amount)")))}}}{{{""=""}}}{{{(matrix(5,1,
     
NUMBER,OF,DIMES,"(larger","amount)")))}}}<font size=5> MINUS 10</font>     OR     {{{(matrix(5,1,

NUMBER,OF,DIMES,"(larger","amount)")))}}}{{{""=""}}}{{{(matrix(5,1,

NUMBER,OF,QUARTERS,"(smaller","amount)")))}}}<font size=5> PLUS 10</font>

</pre>
>>...5 fewer nickels than quarters...<<
<pre>
We know from reading that, that there are more quarters and less nickels, and
that their numbers differ by 5.

So we can also say that either of two ways:

{{{(matrix(5,1,

NUMBER,OF,NICKELS,"(smaller","amount)")))}}}{{{""=""}}}{{{(matrix(5,1,
     
NUMBER,OF,QUARTERS,"(larger","amount)")))}}}<font size=5> MINUS 5</font>     OR     {{{(matrix(5,1,

NUMBER,OF,QUARTERS,"(larger","amount)")))}}}{{{""=""}}}{{{(matrix(5,1,

NUMBER,OF,NICKELS,"(smaller","amount)")))}}}<font size=5> PLUS 5</font>

Since QUARTERS appear in both sentences, we want to let the number of 
quarters be equal to the unknown, say q.

So we choose the two which have quarters on the right side:

{{{(matrix(5,1,

NUMBER,OF,DIMES,"(larger","amount)")))}}}{{{""=""}}}{{{(matrix(5,1,

NUMBER,OF,QUARTERS,"(smaller","amount)")))}}}<font size=5> PLUS 10</font>    AND     {{{(matrix(5,1,

NUMBER,OF,NICKELS,"(smaller","amount)")))}}}{{{""=""}}}{{{(matrix(5,1,
     
NUMBER,OF,QUARTERS,"(larger","amount)")))}}}<font size=5> MINUS 5</font>    

Number of dimes = q+10       AND     Number of q-5

So we have q quarters, q+10 dimes and q-5 nickels
</pre>
>>...The total value of the coins is $4.75...<<
<pre>
Now we turn those 3 numbers of coins all into a money equation.

q quarters are worth  $0.25(q)
q+10 dimes are worth  $0.10(q+10)
q-5 nickels are worth $0.05(q-5)

So we add those together on the left side and set it equal to $4.75:

$0.25(q) + $0.10(q+10) + $0.05(q-5) = $4.75

Drop the dollar marks and move the decimals two places right:

            25q + 10(q+10) + 5(q-5) = 475

Solve that for q, and that will be the number of quarters.
Then substitute for q to find how many dimes q+10 is and 
how many nickels q-5 is. 

Edwin</pre>