Question 65415
Hi modi21
  1) A 60 feet piece of rope is cut into two pieces. One is 12 feet more than three times the other. How long is each piece?
Let the "other peice" be: x
Then "one" is: 3x+12
The two peices added together is:60
(x)+(3x+12)=60
4x+12=60
4x+12-12=60-12
4x=48
4x/4=48/4
x=12
The "other Piece": x=12 ft
The "one": 3x+12=3(12)+12=36+12=48 ft
:
Sanity Check:
If you add the two pieces do you get 60 ft?
12+48=60
60=60 Yes.  Looks ok.
:
 2) If there are 26 coins in a collection of dimes and quarters, and the value of the collection is $4.70, how many dimes and how many quarters are there?
Let the number of quarters be: x
Then the rest of the coins are dimes: 26-x
Therefore, the amount of money (in cents) of quarters is: 25x
Therefore, the amount of money (in cents) of dimes is: 10(26-x)
The total amount of money (in cents) is: 470
25x+10(26-x)=470
25x+260-10x=470
15x+260=470
15x+260-260=470-260
15x=210
15x/15=210/15
x=14
The number of quarters: x=14
The number of dimes: 26-x=26-14=12
:
Sanity check:
If you have 14 quarters and 12 dimes, do you have $4.70?
14($.25)+12($.10)=$4.70 
$3.50+$1.20=$4.70
$4.70=$4.70  It appears we're sane.
Happy Calculating!!!!
funmath