Question

Every evening jenna empties her pockets and puts the change in a jar at the end of the week she had 38 coins all of them dimes and quarters when she added them up she had a totals of $6.95

Answer 1

I imagine the part you left out was "how many of each coin did she have?".  I'm going with that.  The thing is you have to relate the NUMBER of coins to each other, which is very different from the VALUE of the coins.  I could have 1 single quarter, but it's worth 25 cents.  Number vs. value.  If she had 38 coins made up of dimes and quarters, then d + q = 38.  That's the number of dimes and quarters, both still unknown.  A dime is worth .10 and a quarter is .25.  Therefore, .10d + .25q = 6.95.  That's the value of the coins.  Solve the first equation for dimes.  d = 38 - q.  Now we can sub in that value of d into the second equation, so we have only one unknown instead of 2.  $.10(38-q)+.25q=6.95$.  Distribute through the parenthesis to get $3.8-.1q+.25q=6.95$.  Combine all the like terms on both sides to get$.15q=3.15$.  Solve for q and get that q = 21.  So we have 21 quarters.  38-21 = # of dimes, which is 17.  There you go!  Hope that's what you actually needed!  ;)

Answer 2

A) d + q = 38
B)  .1d +.25q = 6.95
Multiply A) by -.1
A) -.1d + -.1q = -3.8The adding B)B)  .1d +.25q = 6.95
.15q = 3.15
21 quarters17 dime
Double-Check********************************************************
17 * .10 + 21 * .25 = 
1.70 + 5.25 = 
6.95